Digitized  by  tine  Internet  Arciiive 

in  2007  with  funding  from 

IVIicrosoft  Corporation 


http://www.arcliive.org/details/abcoflifeinsuranOOwillricli 


THE 


ABC 


OF 


Life  Insurance. 


By   CHARLES    E.  WILLARD. 


^  OF  THE 

\ 

NIVERSITY 

OF          . 

ypOURTH 

EDITION. 

i 

PUBLISHED    BY 

i           THE   : 

SPECTATOR   COMPANY 

1 

New 

York. 

1897 


:t^ERAL 


Entered  in  the  office  of  the  Librarian  of  Congress,  at  Washington,  D.  C,   in 
the  year  1897,  by  The  Spectator  Company,  New  York. 


PREFACE  TO  FIRST  EDITION. 


To  ejcr^iain  and  illustrate  some  of  the  fundamental  and  ele- 
mentary principles  of  Life  Insurance  so  simply  that  they  can 
rpor^vJily  fc  understood  by  men  who  have  not  been  specially 

trained  i>fnathematicians,  or  have  not  had  their  attention  par- 

iCIarly  directed  to  the  theory  and  mathematics  of  Life  Insur- 
ance, 4  tne  aim  of  this  Uttle  book.  For  those  who  already 
possess  this  elementary  knowledge,  there  are  many  excellent 
hand-books  which  carry  the  discussion  much  further,  and 
cover  the  entire  subject  in  the  ablest  and  most  satisfactory 
manner.  But  as  an  introduction  to  these,  a  beginning,  an 
**easy  lesson,"  it  is  hoped  that  the  following  pages  will  have 
their  use.  They  owe  their  existence  to  the  impossibility  of 
findmg  among  the  text-books  already  published  anything 
which  seemed  exactly  adapted  to  this  purpose.         C.  E.  W. 

New  York,  November  i,  1888. 


^ 


PREFACE, TO  FOURTH  EDITION, 


A  demand  for  the  ABC  requiring  a  fourth  edition  to  meet  it 
is  evidence  that  every  year  a  very  considerable  number  of  men 
wish  to  know  what  Life  Insurance  is.  It  is  a  pleasure  to  pre- 
sent to  them  a  revised  and  enlarged  edition  of  the  book,  con- 
taining a  more  extended  discussion  of  net  premiums,  a  presen- 
tation of  the  theory  of  surrender  values  and  surrender  charges,, 
and  a  new  table  of  *' Combined  Experience,  4  per  cent"  net 
premiums,  and,  in  its  references  to  the  actual  conduct  of  the 
business,     informing  to  the  latest  practice.  C.  E.  W. 

New  ^'ork,  November  i,  1897. 


THE 


ABC 

OF 

LIFE    INSURANCE 


CHAPTER  I. 

A   PRELIMINARY  STUDY. 

Insurance,  in  its  simplest  form,  is  indemnity  for  loss. 
Or  it  may  be  described  as  a  method  of  distributing  an 
individual's  loss  among  a  large  number  of  other  persons 
who  are  willing  to  assume  each  his  small  share  of  it,  ia 
return  for  the  certainty  that  if  a  similar  loss  falls  upon  any- 
one of  them,  the  loser,  or  those  dependent  upon  him,  will 
in  like  manner  be  indemnified.  If  a  building  or  stock  of 
goods  is  burned,  so  much  capital  is  destroyed.  If  a  pro- 
ductive human  life  ends,  so  much  capital  in  another  form  is 
destroyed.  For  convenience  in  apportioning  the  loss,  or 
dividing  it  among  those  interested,  the  machinery  and  organ- 
ization of  a  company  are  invoked.  The  company  contracts 
to  pay  the  loss,  the  company  collects  the  premium,  the 
company  pays  the  loss  if  it  occurs.    Consequently,  the  com- 

Note. — It  is  sometimes  flippantly  said  that  insurance  is  simply  a  form 
of  gambling,  the  company  betting  a  large  sum  that  a  certain  loss  will  not 
occur,  the  insured  bettinsf  a  small  sum  that  it  will;  if  the  loss  occurs,  the 
company  pays  the  bet.  In  so  foolish  a  statement  as  this,  only  the  element 
of  chance  is  taken  into  account.  No  consideration  is  had  of  the  fact  that 
the  insured  receives  the  worth  of  his  money,  in  any  event,  in  the  protec- 
tion afforded — the  certainty  that  he  will  be  indemnified  if  the  loss  falls  on 
him.  A  bet  involves  the  payment  of  money  without  any  equivalent  in 
return. 


6  The  A  B  C  of  Life  Insurance, 

pany  is  said  to  insure  each  individual,  but  it  must  be 
remembered  that  the  actual  function  of  the  company  is 
that  of  a  medium  through  which  the  business  is  transacted, 
and  that  the  result  is  simply  the  apportionment  of  such 
individual  losses  as  occur,  among  a  large  number  of  insured 
who  assume  the  payment  of  these  losses  from  year  to  year 
in  order  that  they  may  themselves  claim  a  like  indemnity 
should  the  occasion  arise.  If  this  fact  were  thoroughly 
understood  in  life  insurance,  as  it  is  in  fire,  more  correct 
ideas  of  the  values  of  life  policies  would  prevail  even  among 
those  who  have  no  technical  knowledge  of  the  subject. 

Two  or  three  elementary  principles  constitute  the  foun- 
dation of  all  life  insurance.  They  are  so  simple  that  they 
need  only  to  be  presented  to  be  comprehended  by  any 
person  of  ordinary  intelligence.  Their  practical  application 
to  various  contingencies  may,  and  often  does,  involve 
mathematical  calculations  which  are  not  only  very  lengthy 
but  also  very  intricate.  This  fact  has  thrown  a  veil  of 
mystery  over  the  whole  subject,  which  does  not  properly 
belong  to  it.  One  need  not  be  an  actuary  or  expert 
mathematician  to  have  a  very  fair  knowledge  of  the  funda- 
mental principles.  The  following  example  will  enable  us 
to  study  these  principles  : 

//  should  be  understood  in  advance  that  the  supposed  con- 
ditions of  this  example^  so  far  as  the  rate  of  7nortality  {or 
number  of  deaths  in  a  year)  is  concerned,  are  not  those 
which  we  meet  in  actual  experience.  The  ter7n  of  life  is 
shortened  from  ninety -six  years  to  fifty,  that  the  calculation 
may  be  proportionately  shortened.  The  number  of  deathc^ 
each  year,  and  the  amount  of  insurance  on  each  individual^ 
are  purposely  such  as  to  make  the  calculation  very  simple^ 
and  susceptible  of  instant  verification.     Consequently,  our 


I 


The  A  B  C  of  Life  Insurance. 


results  will  not  be  the  results  of  actual  experience.  The 
premium  will  be  very  much  too  high,  the  annual  cost  of  the 
insurance  very  much  too  great,  the  accumulation  of  reserve 
very  much  too  rapid. 

But  the  two  or  three  elementary  principles  which  we  wish 
to  study  are  perfectly  and  exactly  illustrated.  As  will  be 
shown  later  on,  the  same  process  applied  to  the  conditions 
which  actually  exist,  will  secure  correct  results. 

Bearing  the  above  in  Mind  : 

Let  us  suppose  that  a  company  is  formed  of  i  ooo  men ; 
that  the  age  of  each  man  is  40 ;  that  each  is  insured  for 
$ijop^»that  100  men  will  die  during  the  first  and  each 
succeeding  year  ;*  that  every  man  remains  in  the  company 
until  his  death  occurs ;  that  the  company  receives  nothing 
for  interest  on  money  in  its  hands,  and  pays  nothing  for  the 
expense  of  conducting  the  business.  Suppose,  also,  that 
for  the  sake  of  convenience  these  men  agree  to  pay  a  uni- 
form amount  each  year  so  long  as  they  live,  as  a  premium 
for  the  insurance. 

It  is  evident  that  the  total  amount  of  insurance  to  be 
paid  would  be  1000  x  $1100,  or  $1,100,000. 

It  is  also  evident  that  there  would  be  1000  men  to  pay 
premiums  the  first  year,  900  the  second  year,  800  the  third 
year,  and  so  on.  The  total  number  of  premium  payments 
made  would  be  5500.  Each  payment  therefore  must  be 
$1,100,000  -f-  5500,  or  $200,  which,  upon  our  assumption, 

*  As  a  matter  of  fact,  we  should  expect  that  the  number  of  deaths  among 
1000  men,  age  40,  would  be  but  9  or  10  the  first  year,  and  that  i  or  2  of 
the  1000  men  would  survive  the  age  of  90.  To  make  our  supposition 
conform  to  these  facts  would  extend  our  calculation  over  50  years.  The 
assumption  which  is  made  above,  reduces  the  term  to  10  years,  and  so 
avoids  the  tediousness  of  the  calculation  based  upon  the  longer,  actual 
term. 


8 


The  A  B  C  of  Life  Insurance, 


would  be  the  anriTial,  whole-life  premium  for  an  insurance  ot 
$1  loo  upon  the  life  of  a  man  aged  40. 

The  results  would  be  as  follows : 


i.cxx)  X      $200  = 

100    X    $1,100  =: 


$200,000,  Premiums  received  beginning  of 
110,000,  Losses  paid  durmg 


$90,000,  Amount  in  hand  at  end  of 
900  X      $200  =  $180,000,  Premiums  received  beginning  of 

$270,000,  Total  am't  in  hand  beginning  of 
100  X  $1,100  =     110,000,  Losses  paid  during 

$160,000,  Amount  in  hand  at  end  of 
800  X      $200  =     160,000,  Premiums  received  beginning  of 

$320,000,  Total  am't  in  hand  beginning  of 
100  X  $1,100=     iio.ooo,  Losses  paid  during 

$210,000,  Amount  in  hand  at  end  of 
700  X      $200  =     140.000,  Premiums  received  beginning  of 

$350,000,  Total  am't  in  hand  beginning  of 
100  X  $1,100=     110,000,  Losses  paid  during 

$240,000,  Amount  in  hand  at  end  of 
600  X      $200  =     120,000,  Premiums  received  beginning  of 

$360,000,  Total  am't  in  hand  beginning  of 
100  X  $1,100=     110,000,  Losses  paid  during 

$250,000,  Amount  in  hand  at  end  of 
500  X      $200  =     100,000,  Premiums  received  beginning  of 

$350,000,  Total  am't  in  hand  beginning  of 
loo  X  $1,100=     iio.ooo.  Losses  paid  during 

$240,000,  Amount  in  hand  at  end  of 
400  X      $200  =       80,000,  Premiums  received  beginning  of 

$320,000,  Total  am't  in  hand  beginning  of 
ICO  X  $1,100=     110,000,  Losses  paid  during 

$210,000,  Amount  in  hand  at  end  of 


First 

Year, 

Age  40. 


Second 

Year, 

Age  41. 


Third 

Year, 

Age  42. 


Fourth 

Year, 

Age  43. 


1  Fifth 
\  Year, 
I     ^ge  44- 


) 


Sixth 
S-      ifear, 
Age  45. 


Seventh 

Year, 
Age  46. 


300  X      $200  =       60,000,  Premiums  received  beginning  of 

$270,000,  Total  am't  in  hand  beginning  of 

100  X  $1,100=     110,000,  Losses  paid  during 

$160,000,  Amount  in  hand  at  end  of 

200  X      $200=      40,000,  Premiums  received  beginning  of 

$200,000,  Total  am't  in  hand  beginning  of 

100  X  $1,100=     110,030,  Losses  p-^id  during 


Eighth 

Year, 

Age  47. 


Ninth 

Year, 

Age  48. 


$90,000,  Amount  in  hand  at  end  of  j 

100  X      $200  =      20,000,  Premiums  received  beginning  of     ^      T     th 

$110, oco.  Total  am't  in  hand  beginning  of      Y     Year, 
100  X  $1,100=     110,000,  Losses  paid  during  J       8'  49' 

00 

Now  it  is  evident  that  the  principles  involved  in  fixing 
the  premium  and  collecting  the  necessary  amounts  to  pay 
losses  in  full,  until  the  last  contract  is  met,  must  be  the 
same  whether  the  death  rate  be  9  or  100  per  annum,  and 
the  term  10  or  50  years.  Let  us  see,  then,  what  can  be 
discovered  by  a  study  of  the  above. 

In  the  first  place  it  is  evident  that  the  cost  of  the  insur- 
ance— i.  e.,  the  amount  of  the  losses  in  any  one  year 
divided  by  the  number  of  men  living  at  the  beginning  of 
that  year — ^varies  from  year  to  year,  although  the  annual 
premium  remains  the  same.  The  losses  for  the  first  year 
are  $110,000.  The  number  of  men  to  pay  premiums 
is  1000.  The  cost  of  the  insurance,  therefore,  is 
$110,000-5-1000,  or  $110  per  man.  The  second  year 
the  losses  are  $110,000.  There  are  but  900  men,  how- 
ever, to  pay  premiums,  100  men  having  died.  Conse- 
quently, the  cost  of  the  insurance  is  $110,000 -^  900,  or 
$122.33  P^r  man.  In  the  same  way  the  cost  the  third 
year  is  $110,000.00-7-800,  or  $137.50  per  man;  the 
fourth  year,  $110,000-^700,  or  $157.14  per  man — and 
so  on.     When  we  reach  a  point  where  more  than  one-half 


lo  The  A  B  C  of  Life  Insurance. 

of  the  original  number  of  men  is  dead,  or  will  have  died 
before  the  end  of  the  year,  the  cost  will  exceed  the  premium. 
Thus,  in  the  sixth  year,  the  cost  is  $110,000  -^  500,  or 
$220.00  per  man.  And,  from  this  point,  the  cost  con- 
tinues to  exceed  the  premium  by  an  annually  increasing 
amount  to  the  end. 

It  is  evident,  therefore,  that  a  uniform  or,  as  it  is  usually 
called,  a  "  level "  premium,  involves  the  annual  payment  of 
a  sum  in  excess  of  the  current  cost  of  the  insurance  during 
a  part  of  the  term,  and  the  annual  payment  of  a  sum  less 
than  the  current  cost  of  the  insurance  during  the  remainder 
of  the  term.  Consequently;  whatever  is  overpaid  during 
the  former  portion  of  the  term  must  be  held  in  hand, 
reserved^  to  provide  against  the  deficit  which  would  other- 
wise occur  during  the  latter  part  of  the  term. 

The  same  fact  appears  from  an  inspection  of  the  figures 
above,  without  stopping  to  calculate  the  cost  of  the  insur- 
ance. Thus  we  see  that  the  premiums  received  exceeded 
the  losses  paid  by  $90,000  the  first  year,  $70,000  the 
second  year,  and  so  on  up  to  the  sixth  year.  Then  the 
losses  began  to  exceed  the  premiums,  the  excess  being 
$70,000  in  the  ninth  year,  and  $90,000  in  the  tenth  year. 
If,  now,  the  company  finding  itself  with  $90,000  in  hand  at 
the  end  of  the  first  year,  $160,000  at  the  end  of  the  second 
year,  $210,000  at  the  end  of  the  third  year,  had  overlooked 
the  call  to  be  made  upon  these  funds  in  the  future,  and  had 
spent  or,  through  carelessness  or  misfortune,  lost  some  of 
these  funds,  had  failed  to  keep  the  full  amount  intact,  there 
would  have  been  finally  a  deficit  of  exactly  the  amount  so 
lost  or  spent.  Ten  thousand  dollars  a  year  might  be  spent 
for  several  successive  years  without  affecting  the  company's 
ability  to  pay  its  current  losses,  but  the  time  would  surely 
come  when  the  absence  of  the  money  would  show  itself  in 


The  A  B  C  of  Life  Insurance,  ii 

the  inability  of  the  company  to  carry  its  contracts  of  insur- 
ance to  the  end.  It  is  plain,  therefore,  that  at  the  end  of 
each  year  the  company  would  have  in  its  possession  a  sum 
of  money  which  it  must  carefully  reserve  for  the  future 
fulfillment  of  its  existing  contracts. 

Another  point.  At  the  beginning  of  each  year  (for  the 
above  example  supposes  that  the  company  receives  all  its 
premiums  at  the  beginning  of  the  year),  there  would  be  on 
hand  the  money  brought  over  from  the  preceding  year  plus 
the  premiums  for  the  current  year.  A  portion  of  this 
total  amount  would  have  to  be  held  for  the  payment  of  the 
current  losses  of  this  year.  To  distinguish  this  from  the 
amount  to  be  carried  forward  at  the  end  of  the  year,  we  will 
call  it  the  insurance  reserve.  Since  this  would  be  paid  out 
at  intervals  during  the  year,  as  losses  occurred,  the  sum  left 
in  the  company's  hands  would  slowly  diminish  until,  at  the 
end  of  the  year,  the  insurance  reserve  would  be  entirely  (and 
properly)  expended  in  the  payment  of  losses,  and  only  that 
amount  of  money  which  must  be  held  for  the  future  would 
remain.  This  latter  amount,  since  it  must  be  held  for  a 
series  of  years,  and  might  be  invested  in  interest-bearing 
securities,  we  will  call  the  investment  reserve. 

This  suggests  another  point,  viz.:  that  while  the  reserve  of 
a  policy  may  be  said  to  increase  each  year  that  the  insur- 
ance is  in  force,  this  increase,  so  long  as  premiums  are  paid, 
is  not  an  absolutely  uniform  one.  The  reserve  is  greater  at 
the  beginning  of  the  year,  because  it  includes  both  the 
insurance  and  the  investment  portions  ;  diminishes  during 
the  year,  because  the  insurance  portion  is  expended  grad- 
ually in  the  payment  of  losses ;  but  at  the  end  of  each  year 
is  greater  than  at  the  end  of  the  preceding  year,  because  the 
investment  portion  of  that  year  is  added  to  the  investment 
portion  of  the  preceding  year  or  series  of  years. 


12  The  A  B  C  of  Life  Insurance. 

If  we  divide  the  amount  of  money  in  the  hands  of  our 
supposed  company  at  the  end  of  the  first  year  by  the  num- 
ber of  survivors  at  the  end  of  that  year,  we  have  $90,000  -^ 
900,  or  $100.  This  is  the  amount  of  reserve  for  each  policy 
(or  insurance)  at  the  end  of  the  first  year.  After  the  pre- 
miums have  been  paid  at  the  beginning  of  the  second  year, 
and  before  any  deaths  have  occurred  for  that  year,  the  reserve 
on  each  policy  would  be  $270,000  -5-  900,  or  $300.  At  the 
end  of  that  year  the  reserve  would  be  $160,000  -5-  800,  or 
$200  on  each  insurance.  By  putting  the  figures  of  reserves 
at  the  beginning  and  end  of  several  years  in  parallel  col- 
umns, this  point  will  be  more  clearly  seen : 

Beginning  End 

of  Year.  of  Year. 

Reserve  second  year $3cx)  $20c 

Reserve  third  year 400  30c 

Reserve  fourth  yeai 500  400 

Reserve  fifth  year 600  500 

This  may  be  represented  by  a  diagram  as  follows : 

Fifth  Year. 


2 

\A 

'S 

w 

*s 

a 

•a 

'& 

•F5, 

& 

^ 

& 

Perhaps  the  function  of  the  investment  reserve  may  be 
shown  in  another  way.     Suppose  that  the  company  of  1000 


I^n 


The  A  B  C  of  Life  Insurance.  13 


b  had  agreed  to  pay  each  year  the  exact  cost  of  the 
insurance  for  that  year.  Taking  our  figures  of  cost  on  page 
8,  the  results  would  be  as  follows : 

1,000  X     $110      =$110,000,  Premiums  rec'd beginning  of     ^       p' st    ' 
100  X  $1,100      =     110,000,  Losses  paid  during  i       Year, 

00,  Amount  in  hand  at  end  of  J        &    4  • 


I. 


$122.23  =  $110,000,  Premiums  rec'd  beginning  of  ^  5,          , 

100  X  $1,100       =     110,000,  Losses  paid  during  i  Year, 

—  I  Age  41 

00,  Amount  in  hand  at  end  of  j  ^    "*  ' 

800  X     $137.50  =  $110,000,  Premiums  rec'd  beginning  cf  "^  Th'  d 


1 


00,  Amount  in  hand  at  end  ot  J 


etc.,  etc.,  etc. 


Here,  as  the  increasing  premiums  take  care  of  the  current 
losses  for  each  year,  there  is  no  need  of  carrying  any  amount 
forward  from  one  year  to  another,  and  the  investment  re- 
serve disappears  altogether.  The  insurance  reserve  at  the 
beginning  of  each  year  is  the  full  amount  of  the  expected 
losses  for  that  year.  As  these  losses  occur  and  are  paid  the 
reserve  diminishes,  and  at  any  time  during  the  year  is 
measured  by  the  amount  of  expected  losses  for  the  re- 
mainder of  the  year.  At  the  end  of  the  year,  all  losses 
having  been  paid,  it  is  nothing. 

It  appears  then,  that,  leaving  out  the  question  of  ex- 
penses, the  level  premium  is  made  up  of  two  parts — the 
insurance  portion,  which  pays  the  current  losses  of  the 
year,  and  the  investment  portion,  whose  sole  purpose  and 
use  are  to  keep  the  premium  level.  The  investment  reserve 
(and  this  is  what  is  usually  meant  by  the  term  *'  Reserve  ") 
may  be  defined  as  that  part  of  a  level  or  uniform  premium, 
not  needed  for  current  losses,  which  is  set  aside  for  pur- 


1^  The  A  B  C  of  Life  Insurance, 

poses  of  accumulation,  to  be  used,  with  its  accretions,  im 
payment  of  future  losses. 

Incidentally,  it  should  be  noted  that  the  reserve  of  each  \ 
policy  in  our  example  at  the  tenth  or  final  year,  plus  the 
premium  for  that  year,  is  $iioo,  and  that  the  actual  cost 
of  the  insurance  for  that  year  is  also  $iioo, 

From  this  preliminary  study,  then,  it  is  evident  that  a 
company  must  either  collect  an  annually  increasing  pre- 
mium, correctly  adjusted  to  the  annually  increasing  cost,  or 
must  accumulate  from  a  level  or  uniform  premium  an  invested 
reserve  fund;  that  this  reserve,  if  accumulated,  must  be 
kept  intact  until  needed  for  its  legitimate  purpose,  viz.:  the 
payment  of  such  a  portion  of  each  policy  as  that  policy  has 
contributed  to  it;  that  the  waste  or  loss  of  this  reserve 
means  ultimate  bankruptcy,  on  account  of  the  increasing 
cost  of  the  insurance  for  which  the  level  premium,  without 
the  accumulated  reserve,  does  not  provide ;  and  that  the 
reserve  upon  any  policy  increases  with  the  age  of  that 
policy  or  the  number  of  years  it  has  been  in  force.  We  can 
also  see  that  the  man  who  wishes  insurance  must  continue 

Note. — Another  definition  of  a  reserve  is  "  The  difference  between 
the  present  value  of  the  insurance,  and  the  present  value  of  the  future 
premiums  on  that  insurance."  As  an  illustration  of  this  definition,  our 
example  is  very  crude,  since  it  ignores  the  question  of  compound  interest, 
which  is  the  important  factor  in  determining  present  values.  Neverthe- 
less, it  suggests  the  method  of  calculating  the  reserves  for  insurances  at 
different  ages  and  under  policies  upon  which  premiums  have  been  paid 
for  different  terms  of  years,  as  actually  practiced.  Thus,  in  our  supposed 
company,  at  the  end  of  the  third  year  there  were  700  survivors,  upon  each 
one  of  whom  there  was  an  insurance  of  $1100,  or  a  total  of  $770,000.  The 
total  amount  of  premiums  to  be  paid  during  the  remainder  of  the  term  of 
years  covered  by  the  example  was  $560,000.  Of  course,  if  interest  is  to 
be  ignored,  there  is  no  difference  between  present  and  future  values. 
Consequently,  the  present  values  of  the  insurances  and  of  the  future 
premiums  would  be  their  full  amounts.  The  difference,  $210,000,  is  the 
amount  of  the  reserve  at  the  end  of  the  third  year  given  in  our  example. 


The  A  B  C  of  Life  Insurance,  15 

to  pay  his  premiums  thereon ;  that  the  men  who  die  during 
the  earlier  part  of  the  term  do  not  pay  the  company,  in  pre- 
miums, an  amount  equal  to  the  amount  of  their  insurance ; 
and  that  the  men  who  live  to  the  latter  part  or  end  of  the 
whole-life  term  pay,  in  premiums,  more  than  the  amount 
of  their  insurance. 

Simple  and  elementary  as  is  the  preceding  discussion,  it 
will  repay  careful  study  by  anyone  unfamiliar  with  the 
theory  of  insurance.  And  when  its  points  have  been  mas- 
tered thoroughly,  the  preparation  will  be  ample  for  a 
ready  understanding  of  what  follows  in  this  little  volume. 

Our  illustration  was  based  upon  the  supposition  that  the 
1000  men  were  all  of  the  same  age ;  that  no  other  men  came 
into  the  arrangement;  that  none  of  the  original  number 
dropped  out  by  the  way ;  that  in  each  year  the  number  of 
deaths  was  exactly  what  it  was  expected  to  be  when  the 
company  was  formed ;  that  nothing  was  realized  for  interest 
by  the  investment  of  funds  on  hand ;  and  that  there  was  no 
expense  connected  with  the  transaction  of  the  business.  In 
actual  experience,  men  of  all  ages  are  insured  in  the  same 
company;  new  members  are  continually  coming  in;  old 
ones  are  dropping  out ;  new  sets  of  reserves  are  taking  the 
places  of  those  which  have  been  applied  in  the  payment  of 
losses  or  have  been  withdrawn ;  the  rate  of  mortality  varies 
more  or  less  from  the  tabular  rate ;  interest  is  received  on 
investments;  and  expenses  are  incurred  in  various  ways. 
An  attempt  will  be  made  in  the  following  pages  to  discuss 
some  of  these  matters  briefly  and  simply,  but  to  carry  the 
discussion  only  so  far  as  may  be  necessary  to  an  intelligent 
comprehension  of  the  subject  in  a  somewhat  general  way. 


1 6  The  A  B  C  of  Life  Insurance. 


CHAPTER  II. 
MORTALITY   TABLES. 

If  insurance  is  simply  a  method  of  distributing  or  appor- 
tioning individual  losses  among  a  large  number  of  persons 
who  enter  into  the  arrangement  for  mutual  protection,  the 
fact  will  at  once  suggest  itself  that  each  person  should  pay 
not  only  in  proportion  to  the  amount  of  his  possible  loss, 
but  also  in  proportion  to  the  likelihood  that  that  loss  will 
occur.  Risks  are  classified  for  fire  insurance  according  to 
the  hazard  of  fire.  In  like  manner,  the  life  most  likely  to 
end  should  pay  the  highest  premium.  Asid :  from  the 
special  risk  to  which  any  individual  hfe  may,  at  any  given 
time,  be  subjected  by  reason  of  sickness  or  accident, 
it  is  evident  that  the  older  a  man  grows  the  nearer  he 
is  to  death.  Consequently,  in  determining  the  amount  of 
premiums  which  any  individual  should  pay,  it  is  evident 
that  his  age  must  be  the  prime  factor.  The  first  thing, 
then,  to  be  determined  is  the  effect  of  age  upon  the  rate  of 
mortality — in  other  words,  how  many  deaths  within  a  year 
may  be  expected  among  a  given  number  of  men  of  any  given 
age. 

No  business  in  the  world  has  a  more  reliable  basis  upon 
which  to  make  its  calculations  than  that  of  life  insurance. 
The  rate  of  mortality  among  lives  of  different  ages  has 
been  made  a  matter  of  study  and  record  for  more  than  150 
years.  The  tabulated  results  are  known  as  "  Mortality 
Tables"  or  "Tables  of  Mortality." 


The  A  B  C  of  Life  Insurance,  17 

The  first  used  as  a  basis  for  life  insurance  was  the  North- 
ampton Table.  This  was  formed  by  Dr.  Price  from  obser- 
vations on  the  mortality  in  the  town  of  Northampton,  Eng- 
land, from  1735  to  1780.  This  table  is  no  longer  used  for 
valuations,  and  has  never  been  used  in  this  country. 

The  Carlisle  Table  was  formed  by  Mr.  Milne  from  obser- 
vations in  the  town  of  Carlisle,  England,  from  1778  to  1787. 
It  is  still  in  use  to  a  limited  extent. 

The  Actuaries*  or  Combined  Experience  Table,  published 
in  1843,  was  compiled  from  the  experience  of  seventeen 
English  companies.  It  is  used  in  this  country  as  the  legal 
standard  for  computing  reserves  with  four  per  cent  interest, 
but  in  England  has  been  largely  superseded  by  the  later 
Actuaries'  or  H.  M.  (Healthy  Males)  Table. 

The  Farr  Table,  No.  3,  was  constructed  by  Dr.  Farr  from 
observations  upon  the  mortality  of  the  entire  population  of 
England,  and  was  published  in  1864.     It  is  not  now  in  use. 

The  American  Experience  Table  was  formed  from  the 
experience  of  the  Mutual  Life  of  New  York  by  Mr.  Sheppard 
Homans,  actuary  of  that  company.  It  is  in  general  use  in 
this  country  for  the  computation  of  premiums,  and  as  the 
legal  standard  for  computing  reserves  with  four  and  one- 
half  per  cent  interest. 

The  experience  of  thirty  American  companies  was  tabu- 
lated by  Mr.  L.  W.  Meech,  and  the  results  pubHshed  in 
1 88 1.  This  table  is  generally  known  as  the  Meech  Table. 
It  is  very  valuable  as  a  record  of  actual  experience,  but  is 
not  used  in  valuations. 

For  present  purposes  it  is  necessary  to  give  the  Actuaries* 
and  American  ExperienceTables  only.  These  will  be  found 
on  pages  68,  71  and  72. 

From  the  latter  table  anyone  who  is  interested  to  do  so, 
and  has  the  time  to  spare,  can  substitute  the  proper  figures 


i8  The  A  B  C  of  Life  Insurance. 

for  those  given  in  the  preHminary  example,  and  can  calcu- 
late the  necessary  annual,  whole-life  premium  for  any  age 
without  allowance  for  interest  or  expenses. 

By  dividing  the  number  of  deaths  during  any  year  by  the 
number  of  persons  living  at  the  beginning  of  that  year,  we 
obtain  the  percentage  of  mortality  as  given  in  connection 
with  these  tables. 

From  the  mortality  tables,  also,  by  averaging  the  after-life 
time  of  the  number  of  persons  living  at  any  given  age,  we 
obtain  the  table  of  the  Expectation  of  Life  given  on  page  50. 
This  table  is  interesting,  but  not  particularly  useful.  It  is 
never  employed  in  making  calculations.  The  supposition 
that  the  annual  premium  to  be  paid  by  a  person  of  any 
given  age  is  the  sum  which,  invested  at  four  or  four  and  a 
half  per  cent  during  the  "expectation"  of  that  person, 
would  equal  the  amount  insured ;  or  that  the  present  value 
of  an  insurance,  payable  at  death,  can  be  ascertained  by 
discounting  the  amount  of  the  insurance  at  four  or  four  and 
a  half  per  cent  for  the  number  of  years  represented  by  the 
"  expectation  "  of  the  insured,  is  wholly  erroneous. 

So,  too,  the  average  age  of  a  number  of  Hves  is  not  a 
reliable  measure  of  the  risk  upon  them  all.  Thus,  the 
average  age  of  10  men  aged  98,  and  10  men  aged  30, 
would  be  64  years.  Among  these  20  men  we  should 
expect  at  least  10  deaths  during  the  year,  while  among  20 
men  aged  64  we  should  not  expect  more  than  one  death. 


The  A  B  C  of  Life  Insurance,  19 


CHAPTER  III. 
NET  PREMIUMS, 

A  net  premium  is  one  in  the  calculation  of  which  due 
allowance  has  been  made  for  the  interest  which  a  company 
may  receive  upon  its  investments,  but  with  no  allowance  for 
the  expenses  of  the  business. 

Thus  far  we  have,  for  the  sake  of  simplicity,  neglected  the 
question  of  interest.  But,  since  a  company  may  realize  con- 
siderable amounts  in  the  way  of  interest  upon  judiciously 
invested  funds,  not  needed  for  present  use,  it  is  plain  that, 
in  determining  the  premium  which  it  is  necessary  to  charge, 
due  consideration  of  this  source  of  income  should  be  had. 
Obviously,  the  rate  of  premium  will  be  reduced  by  the  fact 
that  interest  receipts  are  to  be  added  to  the  company's  in- 
come. If  too  great  a  reduction  is  made,  however,  the  pre- 
mium  will  not  be  sufficient.  And,  as  life  insurance  contracts 
may  cover  a  very  long  period,  premiums  must  be  based 
upon  assumptions  which  are  likely  to  be  realized  in  actual  ex- 
perience through  an  indefinite  term  of  years.  With  this  fact 
in  view,  4  per  cent  has  been  taken  as  the  probable  rate  of 
interest,  in  ihe  calculation  of  premiums. 

The  following  explanation  of  the  method  of  calculating  a 
net  annual  premium  for  an  insurance  for  the  term  of  five 
years,  presents  only  the  very  simplest  form  of  such  calcula- 
tions, the  design  being  rather  to  illustrate  principles  and  the 
method  of  their  application,  than  to  present  or  attempt  to 
demonstrate  intricate  mathematical  problems. 


20  The  A  B  C  of  Life  Insurance. 

What  should  be  the  net  annual  premium  (level)  for  an  in- 
surance of  $1000,  for  the  term  of  5  years  only,  upon  the  life 
•of  a  man  aged  40,  according  to  the  American  Experience 
Table  with  4  per  cent  interest  ? 

An  annuity  is  the  recurring  annual  payment  of  a  uniform 
amount.  Consequently  the  annual  premium  is  an  annuity 
paid  by  the  insured  to  the  company.  Manifestly,  there- 
fore, the  proper  method  of  ascertaining  the  required  pre- 
mium is  to  ascertain  the  present  value  of  the  insurance,  and 
then  to  determine  the  amount  of  an  annuity  whose  present 
value  is  equal  to  the  present  value  of  the  insurance.  We 
will  calculate  the  present  value  of  an  insurance  for  $1  and 
then  find  the  corresponding  annuity.  The  latter  will  be  the 
annual  premium  for  an  insurance  of  $1,  which  must  be 
multiplied  by  the  number  of  dollars  of  any  desired  insurance 
to  obtain  the  necessary  premium  therefor. 

In  thiSy  and  in  all  similar  calculations ^  the  premium  is 
considered  payable  at  the  beginning  of  the  year,  and  the  loss 
at  the  end  of  the  year. 

Present  value  of  (or,  in  other  words,  single  premium  for) 
an  insurance  of  $1,  for  a  term  of  5  years,  upon  the  life  of 
a  man  aged  40. 

By  the  American  Experience  Table  (page  68)  it  appears 
that,  out  of  78,106  person  living  at  age  40,  there  will  die 

In  the  I  St  year,  765  persons 


In  the  2d 

"      774 

In  the  3d 

''      785 

In  the  4th 

"      797 

In  the  5th 

"      812 

An  insurance  of  $1,  therefore,  upon  each  person,  would 
require  the  payment  of  $765.00  at  the  end  of  the  first  year, 
$774.00  at  the  end  of  the  second  year,  and  so  on.    From  the 


I 


The  A  B  C  of  Life  Insurance.  21 


table  of  present  values  of  $1   (page  76)  we  find  that  the 
Present  value    at  4  per   cent    of  $1  payable  in   i  year 

is  $0.961538. 
Present  value  at  4  per   cent   of  $1  payable  in  2   years, 

is  $0.924556,  etc. 
Therefore  the   present  value  of  the   above   losses   is  as 
follows  : 

Of  the  $765.00.         $765  X  .961538 ^7355? 

Ofthe    774.00,  774  X  .924556 715.60 

Ofthe    785.00,  785  X  .888996 697.86 

Of  the    797.00,  797  X  .854804 681.28 

Of  the    812.00,  812  X  .821927 667  40 

Total  present  value  of  losses $3,497-72 

If  the  78,106  persons  living  at  the  beginning  of  the  term 
were  to  divide  this  present  value  into  78,106  single  pay- 
ments, to  be  made  at  once,  the  result  would  be  $3,497.72 
-i-  78,106,  or  $0.04478,  and  this  would  be  the  present  value 
of  an  insurance  of  $1,  and  consequently  the  single  pre- 
mium which  each  man  should  pay  in  advance  for  such  an 
insurance. 

But  we  wish  to  find  an  annual  premium  (or  annuity) 
whose  present  value  shall  equal  the  above  present  value  of 
the  insurance.  This  will,  of  course,  be  an  annuity  for  5 
years  contingent  upon  the  lives  of  78,106  persons,  aged  40. 
We  will  first  find  the  present  value  of  such  an  annuity 
for  $1. 

By  the  same  table  of  mortality,  we  find  that  if  each  per- 
son living  at  the  beginning  of  each  year  should  pay  $1, 
the  company  would  receive 

At  the  beginning  ofthe  ist  year,  $78,106.00. 

At  the  beginning  ofthe  2d  year,  77,341.00. 
Lt  the  beginning  of  the  3d  year,  76,567.00. 
Lt  the  beginning  of  the  4th  year,     75,782.00. 

At  the  beginning  of  the  5th  year,    74.985.00. 


22  The  A  B  C  of  Life  Insurance. 

Of  course,  the  present  value  of  the  first  payment  would 
be  the  entire  amount  of  that  payment,  since  it  is  made  at 
once.  The  present  value  of  the  second  payment  would  be 
the  present  value  of  -that  amount  payable  in  i  year ;  of  the 
third,  the  present  value  of  that  amount  payable  in  2  years ; 
and  so  on.  Resorting  again  to  the  table  of  present  values 
of  $1,  we  have 

Present  value  of  the  $78,106.00 $78,106.00  1 

Present  value  of  the    77,341.00  =  $77,341  x  .961538 74,36631 

Present  value  oi  the    76.567.00  =     76,^67  x  ,924556 70,790.48 

Present  value  of  the    75,782.00  =    75,782  x  .888996 67,369.89 

Present  value  of  the    74,985.00  =     74,985  x  .854804 64,097.48 

Total  present  value  of  all  the  payments $354-73°  i^ 

This  total  depends  upon  the  lives  of  78,106  persons — the 
number  living  at  the  beginning  of  the  first  year.     Conse- 
quently, the  amount  depending  upon  the  life  of  any  one  per- 
son must  be  $354,73o-i6^  or  $4.54164.     This,  then,  is  the 
78,106 

present  value  of  an  annuity  of  $1  for  5  years,  contingent 
upon  the  life  of  a  person  aged  40.  This  value  is  much 
larger  than  the  value  of  the  insurance,  which  is  only 
$0.04478.     Consequently  the  required  annuity  or  annual 

premium  will  be  only  .     of  $1,  or  $0.00986.     This  is 

the  net  annual  premium  for  an  insurance  of  $1  for  the 
term  of  5  years  on  a  life  aged  40.  The  premium  for  an 
insurance  of  $1000  would  be  1000  x  $0.00986,  or  $9.86. 

It  will'be  seen  at  once  that,  if  the  term  of  the  insurance 
instead  of  being  limited  to  5  years,  had  covered  the  entire 
term  of  life  according  to  the  American  Experience  Table, 
the  result  would  have  been  the  net  annual,  whole-life  pre- 
mium. 


The  A  B  C  of  Life  Insuraui.^, 


23 


The  following  example  carries  the  premium,  interest,  re- 
serve  and  loss  accounts  through  the  five-year  term,  with  the 
above  premium  and  with  the  rate  of  mortality  shown  by 
the  American  Experience  Table : 

78,106  X     $9.86  =  $770,125  16,  Premiums  rec'd  beginning  of  ' 
30,805.01,  4  per  cent  interest 


765 


77,341 


774 


76,567  X 


785 


^800.930,17,  Total 
765,000.00,  Death  claims  during 


$9.86   : 


$35,930.17,  Reserve  end  of 

762.582.26,  Premiums  rec'd  beginning  of  ^ 


512  43,  Total  beginning  of 
31,940.50,  4  per  cent  interest 


$830,452.93,  Total 
000  =     774,000.00,  Death  claims  during 

$56,452.93,  Reserve  end  of 
).86  =     754,950,62,  Premiums  rec'd  beginning  of  ^ 

$811,403.55,  Total  beginning  of 
32,456  14,  4  per  cent  interest 


$843,859.69,  Total 
Jiooo  =     785,000,00,  Death  claims  during 


75,782  X      $9  86  : 


797 


74.985  X      $9.86  : 


812    X       $1000  : 


$58,859.69,  Reserve  end  of 

747,210.52,  Premiums  rec'd  beginning  of  ' 


$806,070.21,  Total  beginning  of 
32,242.81,  4  per  cent  interest 

$838,313.02,  Total 
797,000.00,  Death  claims  during 


$41,313.02,  Reserve  end  of 

739,352.10,  Premiums  rec'd  beginning  of  ^ 


$780,665.12,  Total  beginning  of 
31,226.60,  4  per  cent  interest 

$811,891.72,  Total 
:     812,000.00,  Death  claims  during 


First 

Year, 

Age  40. 


Second 

Year, 

Age  41. 


Third 

Year, 

Age  42. 


Fourth 

Year, 

Age  43. 


Fifth 
Year, 

Age  44, 


Excess  of  death  claims,  $108.28 

The  excess  of  the  death  claims,  $108.28,  represents  about 
one-seventh  of  a  cent  for  each  person  living  at  the  end  of 


24  The  A  B   C  of  Life  Insurance, 

the  fifth  year.  It  is  impossible  to  express  the  premium 
more  exactly,  in  dollars  and  cents,  than  $9.86.  A  premium 
of  $9.87  would  show  an  excess  of  receipts  over  death  claims 
of  about  $4,207.52,  or  5.6  cents  for  each  person  living  at 
the  end  of  the  term. 

Endowment  policies,  so-called,  are,  strictly  speaking,  en- 
dowment insurance  policies.  To  the  agreement  to  pay  say 
$1000  in  the  event  of  death  within  the  endowment  term,  they 
add  the  agreement  to  pay  $1000  also  provided  the  insured 
shall  live  to  the  end  of  that  term.  Thus  if  A  has  what  is 
usually  called  a  "  twenty-five-year  endowment "  policy,  his 
beneficiaries  will  receive  $1000  if  he  shall  die  within  the 
twenty-five  years,  and  he  will  himself  receive  $1000  if  he 
shall  live  out  the  twenty-five  years.  Manifestly  here  is 
a  double  provision,  the  one  contingent  upon  death  and  the 
other  upon  life.  The  former  is  pure  insurance,  the  latter  is 
pure  endowment. 

What  should  be  the  net  annual  premium  for  a  five-year 
endowment  insurance  of  $1000  upon  the  life  of  a  man  aged 
40,  according  to  the  American  Experience  Table,  with  four 
per  cent  interest  ? 

The  net  premium  for  the  insurance  part  of  this  contract 
we  have  just  found  to  be  $9.86.  If,  then,  we  ascertain  the 
net  premium  for  the  endowment  part  and  add  it  to  the 
$9.86,  the  result  will  be  the  net  premium  for  the  double 
contract. 

Pure  endowment  provides  nothing  for  the  beneficiaries  of 
those  who  die,  but  is  solely  concerned  for  those  who  live. 
Consequently  for  our  immediate  purpose  we  wish  to  know 
the  probable  number  of  persons  who  will  be  living  at  the 
beginning  of  each  year  to  pay  premiums,  and  the  probable 
number  who  will  survive  the  fifth  year  and,  on  the  first  day 
of  the  sixth,  will  be  living  to  claim  the  endowment.     The 


I 


The  A  B  C  of  Life  Insurance,  25 

probable  number  of  premium  payments  will,  of  course,  be 
the  same  as  in  the  preceding  example.  A  glance  at  the 
American  Experience  Table  shows  that  the  probable  num- 
ber of  persons  who  will  live  out  the  five-year  term  and  reach 
age  45  will  be  74,173.  A  pure  endowment  of  %\  for  each 
of  these  will,  of  course,  amount  to  $74,173.  The  method 
of  computing  the  net  annual  premium  necessary  to  provide 
this  amount  is  practically  the  same  with  the  method  of  com- 
puting the  insurance  premium  already  explained,  viz.:  as- 
certain the  single  premium  for  the  pure  endowment,  and 
then  the  equivalent  five-year  annuity. 

Since  no  part  of  the  pure  endowment  is  payable  until  the 
expiration  of  five  years,  while  at  that  time  the  whole  must 
be  paid,  it  is  evident  that  the  present  value  would  be  the 
present  value  at  four  per  cent  of  $r,  payable  in  five  years, 
multiplied  by  the  total  amount  of  the  pure  endowment. 
$745173  X  .821927  =$60,964.79,  the  present  value.  If  the 
78,106  living  at  the  beginning  of  the  term  were  to  divide 
this  into  78,106  single  payments,  to  be  made  at  once,  the 
result  would  be  $60,964.79  -f  78,106  =  $0.78050,  which 
would  be  the  net  single  premium  which  a  man  aged  40 
should  pay  in  advance  to  secure  a  pure  endowment  of  $1  at 
the  end  of  five  years. 

Now,  as  we  found  on  page  22,  the  present  value  of  an 
annuity  of  $1  for  five  years,  contingent  upon  the  life  of  a 
person  aged  40,  is  $4.54164.  This  is  larger  than  the  value 
of  the  pure  endowment,  and  consequently  the  required  an- 
nuity will  be  ^  '^^^  of  $1,  or  $0.17186,  which  is  the  net 
454,164 

annual  premium  for  a  five-year  pure  endowment  of  $1  on 
the  life  of  a  man  aged  40.  The  premium  for  such  an  en- 
dowment of  $1000  would  be,  of  course,  1000  x  $0.17186, 
or  $171.86.     Add  the  pure  insurance  premium,  $9.86,  to 


26  The  A  B   C  of  Life  Insurance, 

the  pure  endowment  premium,  $171.86,  and  we  have 
$181.72  as  the  net  annual  premium  for  an  endowment  in- 
surance (ordinarily  termed  endowment)  of  five  years  on  the 
life  of  a  man  aged  40. 

On  page  23  an  example  carried  the  insurance  part  of  this 
contract  through  the  five  years.  The  subjoined  carries  the 
endowment  part  through  the  same  period. 

78,106  X  $171.86  =  $13,423,297.16,  Prems.  rec'd  beginning  of  ^      p.    . 

536,931.89,  4  per  cent  interest  j.    Year, 

*   Age  40. 
$13,960,229.05,  Reserve  end  of  J 

77,341  X  $171.86  =     13,291,824.26,  Prems.  rec'd  beginning  of  ; 

$27,252,053.31,  Total 

1,090,082.13,  4  per  cent  interest 

$28,342,135.44,  Reserve  end  of 
76,567  X  $171.86  =     13,158,804.62,  Prems.  rec'd  beginning  of  ^ 


Second 
Year, 
Age  41. 


Third 
Year, 
Age  42. 


Fourth 

Year, 

Age  43. 


$4 [,500, 940. 06,  Total 

1,660,037.60,  4  per  cent  interest 

$43,160,977.66,  Reserve  end  of 
75,782  X  $171.86=     13,023,894.52,  Prems.  rec'd  beginning  of 

$56,184,872.18,  Total 

2,247,394.89,  4  per  cent  interest 

$58,432,267.07,  Reserve  end  of 
74,985  X  $171.86=     12,886,922.10,  Prems.  rec'd  beginring  of  ") 

$71,319,189.17.  Total  [     ™^^ 

2,852.767.57,  4  per  cent  interest  1   Age  44. 

$74,171,956.74,  Fund  in  hand  end  of  ) 

r  Amount  required  to  pay  \ 
74,173  X  $1000  =        74,173,000  00,  ■?  endowments  at  the  be-   |      Sixth 

(^  ginning  of  \    Yea'-, 

Age  45. 

Excess  of  endowments,    $1,043.26,  j 

This  excess  of  the  endowments  over  the  fund  in  hand  is 
less  than  a  cent  and  a  half  for  each  person  living  at  age  45 
and  consequently  entitled  to  draw  $1000  from  the  fund. 
The  addition  of  one  cent  to  the  annual  premium  would 


I 

^H  The  A  B   C  of  Life  Insurance.  27 

have  made  the  fund  in  hand  exceed  the  amount  required 
for  the  endowment  by  about  $3275. 

For  the  sake  of  the  demonstration  and  of  the  lessons'* 
which  may  be  learned  from  the  illustration,  we  will  now 
take  the  net  premium,  $181.72,  for  the  pure  insurance 
and  the  pure  endowment  combined,  and  by  an  example 
which  will  be,  of  course,  a  combination  of  that  on  page  23 
and  that  on  page  26,  will  carry  the  premium,  interest,  death 
loss,  reserve  and  endowment  accounts  through  the  five-year 
term. 


78,106  X  $181  72  : 

765  X  $1000  : 

77,341  X  $181.72  : 

774  X  $1000  : 

76,567  X  $181.72  : 

785  X  $1000  : 

75,782  X  $181.72  : 

797  X  $1000  = 


:  $14,193,422.32, 
567,736.90, 

$14,761,159.22, 
:      765,000.00, 

$13,996,159.22, 
:   14,054,406  52, 

$28,050,565.74, 
1,122,022.63, 

$29,172,588.37. 
774,000.00, 

$28,398,588.37, 
■•       13.913.75524, 

$42,312,343.61, 
1,692,493.74, 

$44,004,837.35, 
785,000.00, 

$43,219,837  35, 
:   13,771,105.04, 

$56,990,942.39, 
2,279,637.70, 

$59,270,580.09, 
797,000.00, 

$58,473,580.09, 


Prems.  rec'd  beginning  of 
4  per  cent  interest 

Total  \ 

Death  claims  during 

Reserve  end  of 

Prems.  rec'd  beginning  of  ") 

Total  beginning  of 
4  per  cent  interest 

Total 

Death  claims  during 

Reserve  end  of 

Prems.  rec'd  beginning  of  ' 

Total  beginning  of 
4  per  cent  interest 

Total 

Death  claims  during 

ResTve  end  of 

Prems.  rec'd  beginning  of  ' 

Total  beginning  of 
4  per  cent  interest 

Total 

Death  claims  during 

Reserve  end  of 


First 
.  Year, 
Age  40. 


Second 
Year, 
Age  41. 


Third 
Year, 
Age  42. 


Fourth 
Year, 
Age  43. 


28  The  A  B   C  of  Life  Insurance, 

74.985  ^  $181.72  =     13,626.274.20,  Prems.  rec'd  beginning  of  ^ 

$72,099,854.29,  Total  beginning  of 
2,883,994.17,  4  per  cent  interest 


•ay  "^     Sixth 
in-  >    Year, 
)  Age  45. 


Fifth 
Year, 

$74,983,848.46,  Total  I   Age  44. 

812  X      $1000  =  812,000.00,  Death  claims  during 

$74,171,848.46,  Fund  In  hand  end  of 

C  Amount  required  to  pay 
74,173  X       $1000=   74,173,000.00,  ^endowments    at    begin- 

Cning  of 

Deticit... $1,15154 

This  deficit  is  made  up  of  the  "  excess  of  death  claims, 
$108.28,"  found  on  page  23,  and  the  "excess  of  endowments, 
$1,043.26,"  found  on  page  26.  An  addition  of  five-six- 
teenths of  a  cent  to  the  premium  would  be  more  than  suffi- 
cient to  cover  it. 

A  comparative  study  of  these  three  examples  on  pages  23, 
26  and  27  can  be  made  interesting  and  instructive.  Note  that 
in  the  first  (five-year  term  insurance)  the  reserve  increases 
for  a  while,  then  decreases,  and  finally  is  exhausted  in  the 
payment  of  the  fifth  year's  death  claims ;  that  in  the  second 
(pure  endowment)  the  reserve  increases  steadily  to  the  end 
of  the  term,  and  is  then  exhausted  in  the  payment  of  the 
endowments ;  that  in  the  third  (endowment  insurance)  the 
reserve  steadily  increases  from  year  to  year,  is  always  at  the 
end  of  any  given  year  the  sum  of  the  reserves  for  the  cor- 
responding year  in  the  first  and  second  examples,  and  is 
finally  exhausted  in  the  payment  of  the  fifth  year's  death 
claims  and  of  the  endowments.  Note  also  that  the  reserve 
at  the  end  of  any  year  contains  a  certain  amount,  greater  or 
smaller  as  the  case  may  be,  which  has  been  derived  from 
premium  payments  (with  interest  thereon)  made  by  persons 
who  have  died.  Note  also  the  part  which  compound  inter- 
est plays,  and  the  vital  importance  of  the  interest  earnings 
to  any  company. 


The  A  B   C  of  Life  Insurance.  29 

Still  further,  in  term  insurance,  as  illustrated  in  the  first 
example,  the  fund  in  hand  at  the  end  of  the  fifth  year  is  not 
equal  to  the  total  amount  of  the  outstanding  insurance,  but   ' 
is  equal  to  the  amount  of  insurance  which  is  to  be  paid  as 
death  claims  during  that  year.     Under  the  endowment  in- 
surance the  fund  in  hand  at  the  end  of  the  fifth  year  is  equal 
to  the  total  amount  of  the  outstanding  insurance,  because 
every  person  insured  will  have  a  claim  upon  the  fund  either 
because  of  his  death  during  the  fifth  year  or  because  of  his 
survival  to  the  beginning  of  the  sixth.    Whole-life  insurance 
must  provide  a  fund  at  the  end  of  the  last  year  which  shall 
equal    the   total   amount    of    the   outstanding    insurance, 
because,  by  the  end  of  that  year,   the  few  survivors  who 
began  the  year  will  have  died.     It  is  often  said  that  a 
whole-life  policy  (American  Experience  Table)  is  "  prac- 
tically an  endowment  at  age  96.''     This  is  correct  to  the 
extent  that  the  reserve  under  such  a  policy  at  age  96  will 
equal  the  face  of  the  policy — the  full  amount  of  the  insur- 
ance.    It  has  happened  at  least  once  in  the  history  of  life 
insurance  in  this  country  that  a  man  holding  a  whole-life, 
annual-premium  policy  carried  the  policy  and  paid  the  pre- 
miums until  he  was  96  years  old.     According  to  the  Mor- 
tality Table  he  should  have  been  dead.     He  had  made  all 
the  payments  theoretically  required  under  his  contract,  and 
the  accumulated  reserve  under  his  policy  was  equal  to  the 
full  amount  of  his  insurance.     Very  properly,  the  company 
in  which  he  was  insured  paid  him  his  money  without  waiting 
for  his  actual  demise. 

For  the  sake  of  brevity  a  five-year  endowment  was  chosen 
for  our  example.  In  actual  practice  so  short  endowments  are 
rarely  issued,  and  consequently  the  very  great  disproportion 
between  the  insurance  and  the  endowment  elements  which 

Vears  in  the  preceding  examples  exists  infrequently  in 


30  The  A  B   C  of  Life  Insurance. 

practice.  The  premiums  under  longer  endowments — ten, 
fifteen,  twenty-five  or  more  years- — must,  of  course,  make 
provision  for  a  greater  amount  of  death  claims  during  the 
term,  and  for  a  smaller  amount  of  endowments  at  its  end. 

The  foregoing  illustrations  show  that  a  considerable 
amount  of  work  is  involved  in  determining  the  premium  for 
ordinary  forms  of  insurance  for  one  age  only,  and  for  so 
short  a  term  as  five  years.  It  will  be  seen  at  once  that  the 
computation  of  premiums  for  every  age  and  for  long  terms 
would  be  an  exceedingly  laborious  process.  And  when  dif- 
ferent forms  of  insurance  and  contingencies  involving  more 
than  one  life  are  to  be  considered,  the  mathematical  prob- 
lem may  be  one  of  great  intricacy  and  difficulty.  Log- 
arithms, the  processes  of  algebra,  and  various  devices,  such 
as  **  Commutation  Columns,"  for  lightening  the  labor  of 
computation,  are  employed  by  the  actuaries  or  expert  mathe- 
maticians who  make  the  calculations.  One  who  desires  to 
acquaint  himself  with  the  mathematics  of  Hfe  insurance  can 
find  a  large  number  of  text  books  from  which  to  choose. 
For  our  purpose  it  is  unnecessary  to  follow  the  subject 
further.  Tables  of  net  annual  and  single  whole-life  pre- 
miums will  be  found  on  pages  69  and  73. 


The  A  B  C  of  Life  Insurance .  31 


CHAPTER  IV. 

GROSS  OR  OFFICE  PREMIUMS. 

To  the  net  premium  must  be  added  a  certain  amount 
with  which  to  pay  the  expenses  of  conducting  the  business 
and  to  provide  for  contingencies.  This  amount  is  called 
the  margin  or  loading.  It  is  usually  a  percentage  of  the 
net  premium.  The  loading  and  net  premium  together  con- 
stitute the  gross  or  office  premium — that  which  the  com- 
pany charges  for  the  insurance.  Thus,  from  our  example 
illustrating  the  computation  of  a  net  premium  we  have 

Net  premium  for  a  five-year  term  insurance  of  $1000,  age  40 $9.86 

Margin  or  loading,  say  33^^  per  cent 3.29 

Gross  or  office  premium $13-15 

The  loading  is  usually  a  percentage  of  the  net  premium. 
Its  amount  varies  with  the  form  of  the  insurance  and  the 
objects  which  the  company  has  in  view.  If  it  is  intended 
to  return  a  portion  of  the  premium  in  the  shape  of  divi- 
dends to  the  policyholder,  the  loading  will  be  higher  than 
when  no  such  return  is  contemplated.  Premiums  so  loaded 
are  called  "mutual"  or  "participating"  premiums.  Those 
from  which  no  dividend  is  paid  are  called  "stock  "  or  "  non- 
participating  "  premiums. 

All  annual  premiums  are  supposed  to  be  paid  at  the 
beginning  of  the  policy  year.  If,  by  consent  of  the  com- 
pany, the  premiums  are  paid  semi-annually  or  quarterly,  the 
unpaid  installments  of  the  annual  premium  are  called 
"deferred"  premiums.     Interest  is  charged  on  them,  and 


32  The  ABC  of  Life  Insurance, 

their  amount  is  always  deducted  from  the  amount  of  the 
insurance  in  case  of  a  claim.  As  has  already  been  stated, 
premiums  are  computed  upon  the  theory  that  the  full 
annual  premium  is  paid  at  the  beginning  of  the  year,  and 
the  premiums  are  smaller  than  they  would  otherwise  be. 
Consequently  the  company  is  fairly  entitled  to  retain  the 
unpaid  installments.  This  is  equity  also  between  different 
poh'cyholders.  One  man  pays  a  full  annual  premium  and  dies 
within  three  months.  Another  who  has  taken  his  insurance 
at  the  same  premium  rate,  theoretically,  pays  but  one- 
quarter  of  his  annual  premium  and  also  dies  within  three 
months.  Manifestly  equity  between  these  two  men,  insur- 
ants in  the  same  company,  would  be  observed  by  deducting 
from  the  amount  of  insurance  on  the  latter  the  amount  of 
the  three  unpaid  quarters  of  his  annual  premium. 

An  analysis  of  the  first  year's  whole-life  premium  at  differ- 
ent ages,  showing  what  portion  of  the  net  premium  is  in- 
tended for  death  claims  and  what  for  reserve,  the  amount  of 
a  uniform  loading  of  forty  per  cent  at  all  ages,  and  the 
gross  premium  made  up  of  these  three  items,  is  given  on 
page  70.  Special  attention  is  called  to  the  note  regarding 
this  table  on  page  77. 


The  A  B  C  of  Life  Insurance.  33 


CHAPTER  V. 
RESERVES  J  LOANS  ;  REINSURANCE, 

But  little  need  be  added  to  what  has  already  been  said 
concerning  reserves.  Their  nature  and  function  have  been 
fully  explained.  Nor  is  it  necessary  to  attempt  an  explana- 
tion of  the  method  of  calculating  them.  Remembering  the 
definition  of  a  reserve,  "  the  difference  between  the  present 
value  of  the  insurance  and  the  present  value  of  the  pre- 
miums thereon,"  it  will  be  seen  that  compound  interest  is 
again  an  important  factor.  The  interest  received  upon  the 
fund  representing  the  reserve,  or  upon  the  securities  in 
which  that  fund  is  invested,  may  be  added  to  the  fund  from 
time  to  time,  thus  lessening  the  amount  of  the  principal 
which  must  be  set  aside  for  investment. 

To  put  it  in  another  way,  it  is  evident  that  if  a  company 
is  to  receive  interest  on  its  investments,  it  need  not  reserve 
so  much  money  at  the  present  time  to  meet  a  certain 
amount  of  future  liabilities  as  it  would  have  to  reserve  if  no 
interest  were  to  be  received.  Also,  the  higher  the  rate  of 
interest  the  smaller  the  reserve  required.  If  you  must  have 
$1000  at  the  end  of  a  year,  and  can  get  but  4  per  cent 
interest,  you  must  put  aside  or  reserve  at  the  beginning  of 
the  year  $961.54.  But  if  you  can  get  10  per  cent  you 
need  reserve  only  $909.09.  Reserves  are  usually  calculated 
upon  the  basis  of  the  Actuaries'  Table  with  4  per  cent 
interest,  or  the  American  Experience  Table  with  ^\  per 
cent  interest.  Of  course  those  calculated  on  the  latter 
basis   are    the   smaller.      The   following    table   shows    the 


34  The  A  B  C  of  Life  Insurance, 

reserves  on  a  policy  of  $1000,  issued  at  age  35,  computed 
according  to  the  different  standards: 

American  Experience  Actuaries' 
with  \%,  per  cent  Interest,     with  4  per  cent  Interest. 

End  of  1st  year $9.82  $11.48 

End  of  5th  year S3.20  6134 

End  of  loth  year 1 17-45  133  41 

End  of  15th  year 193-43  21430 

End  of  20th  year 279.59  301.35 

The  percentage  of  difference  decreases  with  the  age  of 
the  policy,  that  is,  the  number  of  years  it  has  been  in  force. 

Tables  of  Reserves  according  to  the  higher  standard,  the 
Actuaries'  Table  of  Mortality  with  4  per  cent  interest,  are 
given  on  pages  74  and  75.  These  are  the  reserves  on  pre- 
mium-paying, ordinary  life  policies.  The  reserves  on  paid-up 
policies  are,  of  course,  the  net  single  premiums  given  in  the 
table  on  page  73. 

There  are  many  forms  of  insurance,  as  will  be  seen  from 
chapter  VI I.  Each  corresponding  form  of  policy  has  its  own 
special  premium,  which  must,  of  course,  provide  for  its  own 
sufficient  reserve.  The  net  premiums  and  reserves  given  in 
the  tables  herewith,  are  those  on  the  most  ordinary  form  of 
life  policy  only.  These  are  sufficient,  in  the  wav  of 
elementary  illustration,  for  the  present  purpose. 

From  the  nature  of  a  reserve,  it  is  always  reckoned  a 
liability  of  the  company.  It  must  be  kept  intact  for  its 
proper  use,  as  already  explained.  If  it  is  not,  and  the  im- 
pairment is  too  great  to  be  made  good,  the  laws  of  the  dif- 
ferent States  require,  under  differing  conditions,  the  winding 
up  of  the  company,  upon  the  theory  that,  although  the 
company  may  be  amply  able  to  pay  its  current  claims,  the 
time  will  surely  come  when  it  will  be  unable  to  do  so. 
Consequently  the  matter  of  suitable  investments  which  shall 
be  safe,  and  at  the  same  time  shall  return  a  fair  rate  of  in- 


The  A  B  C  of  Life  Insurance,  35 

terest,  is  one  of  prime  importance  to  a  company.  The 
laws  of  most  States  prescribe  the  forms  of  investments  which 
a  company  may  make. 

It  should  be  noted  in  passing  that  the  larger  the  reserve 
on  a  poHcy,  the  less  the  amount  which  the  company  has  at 
risk  in  the  insurance.  Thus,  if  the  reserve  on  a  policy  of 
$1000  is  $500,  it  is  evident  that  the  company  need  add  but 
$500  from  its  current  income  to  make  up  the  full  amount 
of  the  insurance.  From  this  point  of  view,  and  regarding 
the  reserve  in  the  light  of  a  deposit  made  by  the  policy- 
holder with  the  company,  Mr.  Elizur  Wright  gave  to  the  re- 
serve the  definition  of  "  self-insurance."  The  actual  loss  to  a 
company  through  death  claims  is  not  the  total  amount  of 
those  claims,  but  the  difference  between  that  amount  and 
the  total  amount  of  the  reserves  credited  to  the  policies 
under  which  the  claims  are  paid. 

The  following  table  shows  the  accumulation  of  the  re- 
serve under  a  policy  of  $1000,  ordinary  Hfe  plan,  issued  at 
age  40.  Column  i  gives  the  portion  of  the  premium  which 
is  set  aside  each  year  for  reserve.  This  diminishes  each 
year,  as  the  actual  cost  of  insurance  increases  each  year. 
Column  2  gives  the  total  amount  of  the  reserve  held  by 
the  company  at  the  end  of  each  year.  Of  course,  at  the  end 
of  the  first  year,  this  is  the  reserve  portion  of  the  first  year's 
premium,  with  one  year's  interest  at  four  per  cent  added.  At 
the  beginning  of  the  second  year,  the  reserve  portion  of  the 
second  year's  premium  is  added  to  the  total  amount  of  reserve 
held  at  the  end  of  the  first  year.  To  this  sum,  one  year's 
interest  at  four  per  cent  is  added,  and  the  total  is  the  reserve 
at  the  end  of  the  second  year.     And  so  on  for  each  year. 

The  net  amount  at  risk  is  obtained  by  subtracting  the  re- 
serve held  by  the  company  at  the  end  of  each  year,  from 
$1000,  the  full  amount  of  the  insurance. 


36 


The  A  B  C  of  Life  Insurance. 


Accumulation  of  Reserve;  Decrease  of  Amount 
AT  Risk. 

Amount  insured,  $1000.  Ordinary  life  plan.  Age  at 
issue,  40.  Reserve  computed  according  to  American  Ex- 
perience Table,  with  four  per  cent  interest. 


Year. 

Reserve  Portion 
of  Premium. 

Accumulated  Re- 
serve at  End  of  Year 

Net  Amount 
at  Risk. 

1st 

$13.06 
12.99 
12.91 
12.82 
12.70 

12.57 
12.40 

12.22 

12.00 

11.73 

11.43 

11.08 

10.71 

10.29 

9.83 

9.34 

8.80 

8.23 

7.65 

6.96 

etc. 

$13.59 
27.65 
42.18 
5720 
72.70 
88.68 

105-13 
122.05 

139.41 
157.19 
175.37 
193-91 
212.80 
232.02 
251-52 
271.30 
291.31 
311-52 
33191 
352.42 
etc. 

$986.41 

972.35 
957-82 
942  80 
927.30 
911.32 
894.87 

877-95 
860.59 
842.81 
824.63 
806.09 
787.20 

2d 

Qd , 

o*-*  • 

4th 

5th 

6th 

7th 

8th      

Qth 

lotn 

nth 

i2th 

iqth 

14th 

767.98 
748.48 
728.70 

15th 

i6th 

17th 

708.69 
688.48 
668.09 

i8th 

19th 

20th 

647-58 
etc. 

etc. 

Premiums  are  sometimes  paid,  by  consent  of  the  com- 
pany, partly  in  cash  and  partly  in  notes.  These  notes  are 
available  as  a  part  of  the  reserve.  The  cash  part  of  the 
premium  is  used  to  pay  expenses  and  current  losses,  and 
the  note  is  laid  away  as  part  of  the  reserve.  Such  notes 
are  called  "  premium  notes  "  and  in  reality  constitute  a  loan 
to  the  policyholder.  The  premium  note  system  has  not 
always  proved  very  satisfactory.  The  notes  accumulate  and 
finally  constitute  a  considerable  lien  upon  the  insurance, 
which  is  deducted  from  the  amount  of  the  insurance  in  case 


The  A  B  C  of  Life  Insurance.  37 

of  claim.  In  companies  whose  dividends  are  large,  the 
accumulation  of  these  notes  is  diminished  by  applying  the 
dividends  towards  their  payment.  There  are  very  few  com- 
panies at  present  which  use  the  note  system. 

Policies  having  a  large  reserve  value  are  sometimes  used 
as  collateral  for  loans.  Their  main  value  for  such  purpose 
lies  in  the  reserve.  The  insurance  itself  is  payable  only 
upon  the  happening  of  a  certain  contingency,  /.  ^.,  the  death 
of  the  insured,  and,  of  course,  constitutes  a  very  indefinite 
form  of  security.  Endowments  (policies  payable  when  the 
insured  reaches  a  certain  age,  or  at  prior  death)  are  more 
available  as  collateral  security,  but  even  here  the  definite 
value  of  the  collateral  is  largely  dependent  upon  the  amount 
of  the  reserve. 

The  amount  of  money  allowed  by  a  company  for  the 
surrender  of  a  policy  is  governed  by  the  reserve,  unless 
the  insured  is  in  poor  health.  In  that  case  the  prospect  of 
his  early  death,  which  would  make  the  policy  a  claim  for 
the  full  amount  of  the  insurance,  would  give  an  added 
present  value  to  the  policy.  It  is  evident,  however,  that, 
if  the  insured  be  in  good  health,  the  reserve  on  his  policy 
represents  his  entire  equity  in  the  insurance,  since  the 
remaining  portion  of  his  premiums  has  been  used  for  the 
payment  of  current  losses  and  expenses.  As  a  matter  of 
fact,  the  reserve  represents  more  than  the  entire  equity  of 
the  policyholder  and,  for  that  and  other  reasons,  should  be 
subject  to  a  "  surrender  charge."  This  will  be  considered 
in  a  subsequent  chapter. 

In  cases  of  reinsurance,  the  reserve  is  again  the  important 
element  of  the  transaction.  If  a  company  wishes  or  is 
forced  to  withdraw  from  business,  it  sometimes  reinsures  its 
risks,  i.  <?.,  transfers  them  to  another  company.  This  latter 
company  assumes  the  contracts  of  the  former,  and  charges 


38  The  A  B  C  of  Life  Insurance, 

the  same  premium  tor  the  insurance  which  each  policyholder 
was  paying  the  original  company.  To  enable  it  to  do  this, 
the  reserve  fund  accumulated  by  the  original  company 
must  be  transferred  to  the  reinsuring  company,  else  the  lat- 
ter company  would  be  the  loser  by  the  transaction,  by  at 
least  the  deficiency  of  the  reserve.  Consequently,  a  com- 
pany which  has  impaired  its  reserve  to  any  considerable 
extent  cannot  reinsure  its  risks. 

The  reserve  is  sometimes  called  the  "reinsurance"  re- 
serve. 


The  A  B  C  cf  Life  Insurance,  39 


CHAPTER  VI. 

SURPLUS  J  DIVIDENDS, 

The  surplus  of  a  company  is  the  excess  of  its  assets  over 
its  liabilities.  The  former  include  such  real  estate  as  the 
company  may  own,  cash  on  hand  and  in  course  of  trans- 
mission, stocks,  bonds,  mortgage  loans,  loans  on  collaterals, 
premium  notes,  accrued  rents  and  interest,  and  deferred 
premiums  less  the  loading.  The  liabilities  include  the  re- 
serve, unpaid  death  claims  and  all  unpaid  bills  or  current 
obligations.  The  reserve  will  be  the  largest  item  of  liability  , 
unless  the  company  has  been  doing  business  but  a  very 
short  time.  If  it  is  calculated  upon  a  At\  per  cent  basis 
it  will  be  smaller  than  if  upon  a  4  per  cent  basis. 
Consequently,  the  surplus  at  4^  per  cent  will  be  larger  than 
at  4  per  cent,  by  exactly  the  difference  between  a  4  per 
cent  and  a  4^  per  cent  reserve.  In  some  of  the  older  and 
larger  companies  this  difference  amounts  to  several  million 
dollars. 

The  principal  sources  of  surplus  are  ordinarily: 
A  lower  rate  of  mortality  than  was  assumed  in  the  compu- 
tation of  the  premiums  ; 

A  higher  rate  of  interest,  actually  received,  than  was 
assumed  in  that  computation ;   and 

The  use  of  a  less  amount  of  money  for  expenses  than  was 
provided  for  by  the  loading  of  the  premiums. 

If  exactly  the  tabular  rate  of  mortality  were  experienced, 
exactly  the  assumed  rate  of  interest  were  realized,  and  ex- 


40  The  A  B  C  of  Life  Insurance. 

actly  the  amount  of  the  loading  were  used  for  expenses,  the 
company  would  at  all  times  have  its  reserve  on  hand,  but 
not  a  dollar  of  surplus.  (Surplus  and  reserve  should  be 
carefully  distinguished.  They  are  entirely  separate  and  dis- 
tinct. One  is  an  asset,  the  other  a  liability.  One  can  be 
used  for  such  purposes  as  the  company  thinks  best.  The 
other  should  be  used  only  in  the  manner  and  for  the  pur- 
pose which  have  been  so  fully  explained  and  illustrated  in 
the  preceding  pages.) 

The  rate  of  mortality  in  any  well-managed  company 
should  be  less  than  the  assumed  or  tabular  rate. 

The  rate  of  interest  has  for  many  years  averaged  more 
than  4  per  cent.  For  at  least  ten  years  subsequently  to 
1865  it  averaged  8  per  cent.  Its  constant  tendency,  how- 
ever, is  to  become  lower.  Consequently,  one  exceedingly 
important  factor  in  producing  surplus  in  earlier  years  has 
grown  less  and  less  important  in  later  years. 

The  amount  used  for  expenses  ought  not  to  equal  the 
loading  in  any  company  which  has  a  considerable  amount 
of  business,  especially  if  the  premiums  are  heavily  loaded. 

After  retaining  a  surplus  sufficiently  large  to  provide  for 
contingencies,  it  is  customary  among  companies  which  issue 
policies  on  the  mutual  or  participating  plan  to  divide  the 
remainder  of  the  surplus  among  such  of  its  policyholders  as 
are  entitled  to  share  in  it.     This  is,  in  reality,  the  return  of 


Note— Formerly,  if  a  policy  "  lapsed,"  the  entire  reserve  was  forfeited 
to  the  company,  and  thus  no  inconsiderable  additions  were  made  to  the 
surplus.  Now,  however,  a  more  equitable  practice  prevails,  and  the  ad- 
ditions to  the  surplus  from  this  source  are  now  less  than  formerly.  In 
general,  the  most  considerable  gain  from  lapsed  policies,  at  present, 
arises  from  forfeitures  of  contingent  dividends  and  a  portion  of  the  reserve 
under  the  "  Tontine  "  system  as  explained  on  page  57.  As  the  Tontines 
form  a  special  class,  they  are  not  included  above  in  considering  sources  of 
surplus. 


The  A  B  C  of  Life  Insurance,  41 

an  overcharge,  but  it  is  customary  to  call  it  the  payment  of 
a  dividend. 

The  principal  plans  upon  which  dividends  are  distributed 
are  the  percentage  plan  and  the  contribution  plan.  The 
former  allows  dividends  as  a  percentage,  either  on  the 
amount  of  the  insurance  or  on  the  sum  of  all  premiums 
paid.  The  latter  takes  account  of  the  sources  of  surplus 
and  of  the  amount  which  each  individual  policy  has  contrib- 
uted. For  example:  if  the  mortality  has  been  but  80  per  cent 
of  the  tabular  rate,  20  per  cent  of  the  cost  of  the  insurance 
under  A's  policy  is  credited  to  him ;  if  interest  has  been  6  per 
cent,  instead  of  4  per  cent,  2  per  cent  upon  the  reserve 
under  his  policy  is  also  credited  A ;  if  the  expenses  have 
been  90  per  cent  of  the  loading,  10  per  cent  of  the  loading 
of  A^s  premium  is  also  credited  him.  The  sum  of  these 
three  items  is  the  amount  of  the  dividend  received  by  A. 
This  plan,  now  almost  universally  adopted,  was  devised  by 
Mr.  Sheppard  Homans,  assisted  by  Mr.  D.  P.  Fackler. 

Dividends  are  paid  sometimes  in  cash,  sometimes  in 
reduction  of  the  next  year's  premium,  sometimes  by  the 
addition  of  a  certain  amount  of  insurance  to  the  original 
amount  of  the  policy.  In  the  latter  case  they  are  known  as 
"  reversionary  "  dividends. 

The  frequency  with  which  the  accumulated  surplus  is 
divided,  and,  consequently,  the  periods  at  which  dividends 
are  declared,  vary  with  different  forms  of  policies  and  the 
practice  of  different  companies.  Sometimes  dividends  are 
paid  annually.  In  other  instances,  as  under  policies  written 
upon  the  twenty-year  distribution  plan,  they  are  paid  once 
in  twenty  years,  and  only  upon  such  policies  as  are  then  in 
force. 


42  The  A  B   C  of  Life  Insurance. 


CHAPTER   VII. 
TERMINATIONS  AND  SURRENDER  VALUES. 

Policies  of  insurance  which  from  any  cause  cease  to  be  in 
force  are  said  to  "  terminate."  The  methods  of  termina- 
tion may  be  classified  as  follows :  By  "  death,"  when  the 
policy  becomes  a  claim  on  account  of  the  death  of  the  in- 
sured; by  "maturity/*  when  an  endowment,  for  instance, 
becomes  payable  because  the  end  of  the  endowment  period 
has  been  reached;  by  " expiry,"  when  a  term  insurance  has 
been  carried  to  the  end  of  the  term  for  which  it  was  issued 
and  consequently  is  no  longer  in  force ;  by  "  lapse,"  when 
the  policy  is  terminated  solely  by  reason  of  the  non-pay- 
ment of  a  stipulated  premium  when  due ;  by  "  surrender," 
•  when  the  legal  liability  of  the  company  under  the  policy  is 
voluntarily  canceled  by  the  insured  and  beneficiary  for  a 
consideration  allowed  by  the  company,  which  consideration 
is  called  the  "  surrender  value." 

Evidently  the  payment  of  a  death  claim  or  an  endowment 
when  due  meets  the  full  measure  of  a  company's  responsi- 
bility under  such  a  policy.  From  what  has  been  said  in  the 
preceding  pages  the  reader  will  understand  that  a  five-year, 
ten-year  or  any  other  purely  term  insurance  which  has  ex- 
pired has  no  subsequent  value.  But  in  the  case  of  a  lapsed 
whole-life  or  endowment  policy,  for  example,  to  what  con- 
sideration in  the  way  of  a  surrender  value  is  the  insured 
equitably  entitled? 

It  is  not  at  all  unusual  for  such  a  person  to  say,  "  The 


I 


The  A  B   C  of  Life  Insurance.  43 


company  has  paid  out  nothing  under  my  policy.  I  have 
not  died  nor  has  my  pohcy  matured ;  consequently  my  in- 
surance has  cost  the  company  nothing.  I  ought  to  have 
my  premiums  returned  to  me,  to  say  the  least,  and  even  then 
the  company  will  have  had  the  interest  on  my  money."  The 
obvious  answer  to  this  is  that  the  risk  carried  by  any  com- 
pany is  the  total  amount  of  its  insurance  in  force,  not 
simply  that  portion  of  the  total  amount  which  becomes  a 
claim  by  death  or  maturity ;  that  each  policy  is  a  part  of 
the  aggregate,  and  consequently  contributes  to  the  total 
cost  as  well  as  to  the  total  income;  and  that  while  the 
total  loss  is,  so  to  speak,  individualized  by  the  death  of  cer- 
tain persons,  nevertheless  the  cost  actually,  and  properly, 
falls  on  all  the  insured,  those  who  do  not  die  receiving  the 
full  worth  of  their  money  in  the  protection  afforded.  The 
aggregate  of  all  the  premiums  paid  by  all  the  insured  is 
used  to  pay  expenses  and  death  losses  so  far  as  it  is  re- 
quired for  that  purpose,  and  from  each  individual  premium 
is  taken  its  proper  proportion. 

On  the  other  hand,  in  the  early  history  of  life  insurance 
no  surrender  value  was  allowed  in  case  of  lapse.  Under 
this  practice  no  account  was  taken  of  the  fact  that,  after  de- 
ducting the  cost  of  his  insurance  and  his  proper  contribu- 
tion to  expenses,  the  insured  had  still  paid  to  the  company 
an  amount  in  excess  of  both  these  items,  which  was  repre- 
sented by  the  "  reserve,"  and  for  which  at  the  date  of  lapse 
he  had  received  no  consideration.  Gradually  this  fact  and 
the  equities  involved  in  it  were  recognized,  and  out  of  this 
recognition,  stimulated  to  some  extent  by  legislation  and  to 
a  much  larger  ex'ent  by  the  competition  of  the  companies 
for  business,  has  grown  the  elaborate  modern  system  of  sur- 
render values. 

In  discussing  this  system  let  us  use  for  the  purpose  of 


44  Tf'i^  A  B   C  of  Life  Insurance, 

illustration  the  whole-life  policy  only,  while  recognizing  the 
fact  that  endowments,  annuities  and  other  forms  are  issued' 
by  the  same  company,  and  that  what  is  said  concerning  the 
whole-life  policy  may  require  some  modification  in  apply- 
ing the  general  principle  to  a  specific  instance  of  another 
form  of  insurance. 

What  is  the  exact  status  of  both  parties  to  an  ordinary 
whole-life  contract?  The  insured  has  requested  in  his 
"application"  that  the  company,  in  consideration  of  the 
annual  paymen*^  of  a  specified  premium  so  long  as  the  in- 
sured shall  live,  shall  bind  itself  to  pay  a  specified  amount 
to  the  designated  beneficiary  whenever  the  insured  shall  die. 
The  company,  in  compliance  with  this  request,  has  issued  ai 
contract  (policy)  by  which  it  is  so  bound.  The  presumption 
is  that  this  is  a  contract  which  will  be  maintained  during 
the  lifetime  of  the  insured,  and  the  company  relies  upon  the 
annual  payments  of  premium  as  a  revenue  from  which  it 
will  derive  a  certain  contribution  to  the  payment  of  its 
death  losses,  another  to  the  payment  of  its  expenses^, 
another  to  the  making  of  a  reasonable  profit  from  its  busi- 
ness. The  company  has  exactly  the  same  right  to  expect ; 
these  things  which  the  insured  has  to  expect  the  prompt 
payment  of  his  loss  when  it  occurs.  If,  now,  the  policy- 
holder fails  to  pay  all  the  premiums  contemplated  by  his 
contract,  the  company  is  at  once  cut  off  from  that  source  of 
income  and  profit,  and,  at  considerable  expense,  must  seek 
another  customer  to  replace  the  one  which  it  has  lost.  The 
policyholder  has  had  his  insurance  at  its  cost  plus  expenses, 
and  has  an  equity  in  the  accumulated  reserve.  That  he 
"  owns  "  the  specific  amount  of  the  reserve  on  his  individual 
policy,  as  has  been  vehemently  asserted  in  some  quarters, 
cannot  be  true.  In  the  first  place,  there  has  never  been  a 
year  in  which  the  reserve  credited  to  his  policy  has  been 


The  A  B   C  of  Life  Insurance,  45 

made  up  entirely  of  his  own  money  with  interest  accretions, 
and  consequently  it  is  not  true  that  that  reserve  stands 
e  xactly  in  the  light  of  a  deposit  made  by  fiimself  out  of  his 
own  funds.  Part  of  the  reserve  was  contributed  by  men 
who  died  in  prior  years.  If  the  reader  is  interested  to  work 
out  an  illustration  of  this  fact  for  himself,  let  him  take  any 
one  of  the  three  examples  on  pages  23,  26  and  27.  and  note 
the  number  and  amount  of  premiums  in  excess  of  the  actual 
cost  of  the  insurance  paid  each  year  by  those  who  die  dur- 
ng  that  year,  and  compute  their  aggregate  with  compound 
nterest  accretions.  Of  course,  under  the  pure  endowment, 
page  26,  since  there  is  no  insurance  there  can  be  no  cost  of 
insurance,  and  the  reserve  at  the  end  of  each  year  includes 
every  cent  which  has  been  paid  by  all  those  who  have  died. 
If  the  reader  has  followed  the  discussion  carefully  from  the 
first  page  to  the  current  one,  he  will  readily  understand  that 
the  amount  of  contribution  to  the  reserve  by  those  who  have 
died  will  vary  very  largely  with  the  form  of  policy  and  the 
length  of  time  during  which  the  insurance  has  been  in  force, 
being  in  some  cases  of  considerable,  and  in  others  of  incon- 
siderable, importance.  But  that  any  such  contribution,  of 
greater  or  of  less  amount,  has  been  made,  is  sufficient  to 
nuUify  the  alleged  **  ownership  "  of  the  reserve.  The  fact 
is  that  the  insured  agrees  to  pay  so  much  a  year  for  so  much 
insurance ;  as  a  rule  he  knows  little  of  the  theory  or  practice 
of  the  business,  and  concerns  himself  less.  He  has  a  very 
hazy  idea  of  a  ''reserve,"  and  wouldn't  know  what  was 
meant  if  he  should  be  told  that  he  "  owned  "  it ;  he  does 
not  buy  a  reserve  nor  stipulate  for  such  a  purchase ;  he  ex- 
pects the  company  to  live  up  to  its  contract  and  to  treat 
him  fairly ;  and,  even  if  he  expected  or  desired  it,  the  com- 
pany could  not  sell  him  the  ownership  of  his  reserve  unre- 
stricted by  conditions  and  enforceable  at  any  time.    Conse- 


46  The  A  B   C  of  Life  Insurance, 

quently  what  shall  be  done  with  the  reserve  under  a  lapsed 
policy  is,  apart  from  legislative  interference,  purely  a  ques- 
tion of  equity  between  the  two  parties  to  the  contract. 

In  determining  what  is  equity,  the  company  on  its  sirle 
must  at  least  consider  another  question  in  some  respects  far 
more  important  than  the  loss  of  income  and  profit  in  case 
of  lapse.  The  man  who  is  in  sound  health  will  be  likelier 
to  surrender  his  insurance  than  the  man  who  has  reason  to 
believe  that  his  health  is  impaired  and  his  chance  of  life 
diminished.  This  is  simply  human  nature,  and  in  this  re- 
spect the  "  selection,"  as  it  is  termed,  is  always  against  the 
company.  By  this  it  is  not  meant  that  none  but  '*  good  risks  '* 
will  allow  their  insurance  to  terminate,  Financial  difficul- 
ties, altered  circumstances,  the  death  of  beneficiaries  for 
whom  consequently  the  provision  of  insurance  is  no  longer 
needed,  a  multitude  of  reasons  for  discontinuing  insurance 
affect  alike  the.  good  and  the  poor  risks,  and  in  many  cases 
are  imperative.  But  where  there  is  any  choice  in  the  mat- 
ter, the  man  of  impaired  health,  because  he  values  his  insur- 
ance the  more,  will  make  the  greater  effort  to  continue  it. 
The  consequent  result  of  a  high  rate  of  lapse  is  to  reduce 
the  average  standard  of  the  risks  which  remain,  and  thus  to 
increase  the  death  rate,  a  consideration  of  the  utmost  im- 
portance. 

There  are  other  questions  which  might  be  considered  if 
this  little  book  were  intended  as  an  exhaustive  discussion  of 
the  topics  presented,  but  for  its  less  ambitious  purpose  it  is 
not  necessary  to  take  them  up.  Enough  has  been  said  to 
make  it  evident  that,  as  a  matter  of  self-protection  to  the 
company,  and,  in  fact,  of  equity  between  the  retiring 
policyholder,  the  company  and  those  who  remain,  a  reason- 
able forfeit  might  well  be  demanded  by  the  company  from 
the  man  who  lapses  his  policy.     This  forfeit  is  known  as  a 


■ 


7 he  A  B   C  of  Life  Insurance,  47 


surrender  charge."  What  should  be  the  amount  of  this 
charge  is  a  vexed  question.  Eminent  actuaries  differ  in 
regard  to  it,  the  practice  of  the  companies  is  not  uniform, 
£,nd  the  laws  of  such  States  as  attempt  to  regulate  the  mat- 
ter by  statute  are  widely  apart  in  their  provisions.  Without 
a.ttempting  to  decide  or  even  to  suggest  where  doctors  fail 
jto  agree,  let  us  consider  for  a  moment  in  what  form  that 
portion  of  the  reserve  which  remains  after  deducting  the 
surrender  charge,  shall  be  available. 

It  has  been  said  that  life  insurance  companies  exist  for 
,  the  purpose  of  selling  life  insurance  and  not  of  buying  it. 
Tliat  used  to  be  true,  but  the  modern  surrender-value  sys- 
jtem  has  largely  modified  the  actual  functions  of  an  insurance 
company.  Theoretically,  if  A  has  purchased  a  policy  of  life 
insurance,  and  B  an  endowment,  and  C  an  annuity,  they 
would  be  entitled,  in  the  event  of  lapse,  to  receive  as  a  con- 
sideration for  their  respective  reserve  equities  an  equivalent 
amount  of  their  respective  forms  of  insurance  upon  which 
no  further  payment  of  premium  would  be  necessary.  Thus 
iVs  reserve  equity  would  be  applied  as  a  single  premium  to 
purchase  insurance  payable  at  his  death,  B's  would  be 
i  applied  as  a  single  premium  to  buy  an  endowment  payable 
at  the  same  date  at  which  his  original  endowment  would 
have  been  payable,  and  C's  to  purchase  an  annuity  payable 
[It  the  same  time  and  under  the  same  conditions  with  his 
original  annuity.  All  of  these  policies  would  be  known  as 
**  paid-up"  policies.  Their  amount  would  necessarily  be 
less  than  the  amount  of  the  originals. 

Example. — A  took  a  whole  life  policy  of  $5000  at  age 
40,  carried  it  ten  years  and  lapsed.  To  what  amount  of 
paid-up  insurance  would  he  be  entitled  as  a  surrender 
value  ? 


4^  The  A  B   C  of  Life  Insurance. 

Reserve  on  such  a  policy  (see  table  on  page  75) 
would  be  5  X  $162.97  or $814.85 

Surrender  charge,  say  10  per  cent 81.49 

'  — -^— ^^— — — 

Net  equity  in  reserve $7  3336 

A  at  the  time  of  lapse  is,  of  course,  50  years  old.  Single 
premium  for  insurance  at  that  age  is  $481.92  for  each  $1000 
(see  table  on  page  75).     Consequently  A's  equity  would 

purchase  ^^^^    of  $1000,  which  would  be  $1520. 
48162 

In  this  case,  then,  instead  of  having  a  policy  of  $5000 
on  which  he  must  pay  a  premium  every  year,  A  would  have 
a  policy  of  $1520  on  which  he  would  have  to  pay  no  more 
premiums. 

There  is  another  way  in  which  the  reserve  equity  might 
be  appHed  to  the  purchase  of  insurance.  Instead  of  issu- 
ing a  paid-up  policy  for  a  less  amount  but  in  force  until 
terminated  by  the  death  of  the  insured,  the  company  might 
continue  the  full  amount  of  the  insurance  (in  the  example, 
$5000,)  in  force  during  such  a  term  as  the  reserve  equity 
would  pay  for.  If  the  insured  should  die  during  that  term 
his  beneficiaries  would  be  paid  the  full  amount  of  the  policy, 
but  if  he  should  outlive  the  term,  the  policy  would  ter- 
minate by  expiry  and  the  insurance  would  cease.  An 
arrangement  of  this  description  is  called  "extended'' 
insurance. 

It  is  also  evident  that  any  person's  reserve  equity  under 
one  form  of  insurance  might  be  used  to  purchase  an  equiv- 
alent amount  of  paid-up  or  extended  insurance  of  another 
form.  Thus  B  might  have  the  reserve  equity  under  his 
endowment  policy  applied  to  the  purchase  of  paid-up 
whole-life  insurance. 

The   above   surrender  values   which,  not  so  very  many 


The  A  B   C  of  Life  Insurance,  49 

years  ago,  were  about  all  that  were  offered  or  allowed  by 
the  majority  of  companies — unless  in  exceptional  instances 
or  under  very  special  forms  of  policies — have  in  recent  times 
been  supplemented  and  largely  superseded  by  the  popular 
cash  surrender  value.  Practically  there  are  many  cases  in 
which  the  insured,  when  he  lapses  his  policy,  has  no  further 
need  for  insurance,  but  has  urgent  need  for  money,  and  in 
which  to  insist  upon  applying  his  reserve  equity  to  the  pur- 
chase of  any  form  of  insurance,  and  to  refuse  to  give  it  to 
him  in  cash,  works  a  hardship.  Consequently  a  policy 
which  provides  for  a  cash  value  is  attractive  to  anyone  who 
thinks  he  may  sometime  need  the  cash  more  than  the  insur- 
ance, and  would  rather  have  a  contract  right  to  call  for  the 
cash  than  to  be  obliged  to  negotiate  for  it  and  perhaps  find 
the  company  unwiUing  to  pay  it.  Partly  as  a  concession  to 
possible  necessity  on  the  part  of  the  insured  and  partly  as 
an  effective  method  of  competing  for  business,  the  com- 
pany began  to  make  cash  surrender  values  a  feature  of  more 
and  more  of  their  policies  until  at  the  present  time  a  policy 
without  such  provision  is  rather  the  exception  than  the  rule. 
In  the  beginning  a  good  deal  of  caution  was  exercised  on 
the  theory  that  it  might  not  always  be  convenient  for  a  com- 
pany to  pay  the  reserve  equity  in  cash.  It  is  necessary  that 
a  company  should  obtain  a  certain  rate  of  interest  on  its 
assets,  and  it  cannot  afford  to  keep  on  hand  too  large  an 
amount  of  uninvested  money.  Investments  must  also  be 
made  in  the  best  class  of  securities  and  in  those  having  a 
long  time  to  run.  A  life  insurance  company  must  also  pro- 
tect itself  against  the  results  of  a  financial  panic  and  must 
not  open  the  way  for  a  possible  "  run  "  upon  itself  by  treat- 
ing its  reserves  practically  like  individual  deposits  in  a  bank. 
These  and  other  similar  arguments  seemed  to  have  great 
weight  at  first,  and  in  consequence  cash   values  were  not 


50  The  A  B   C  of  Life  Insurance, 

allowed  whenever  the  policies  might  lapse,  but  only  at  stated 
intervals,  five,  ten,  fifteen  years,  and  so  on.  Moreover,  the 
portion  of  the  reserve  which  would  be  paid  in  cash  was 
smaller  than  the  amount  which  would  be  applied  to  pur- 
chase insurance,  in  other  words,  when  cash  was  paid  the 
surrender  charge  was  increased.  But  gradually  all  this  has 
been  done  away  with.  This  may  be  partly  due  to  the  fact 
that  the  evil  effects  which  were  anticipated  from  the  free  use 
of  cash  surrender  values,  were  not  realized,  and  partly  to  the 
efforts  of  the  different  companies  to  outdo  each  other  in 
competition  for  patronage,  but,  whatever  the  reason,  cash 
values  are  to-day  the  rule  among  the  '^  options  "  given  by 
policy  contracts  whenever  the  policy  lapses,  and  surrender 
charges  have  diminished  in  proportion.  Practice  in  this 
case,  as  in  many  others,  does  not  conform  to  theory.  It  is 
the  aim  of  this  discussion  to  present  the  latter  clearly.  He 
who  seeks  an  exemplification  of  the  former  by  examining 
the  current  forms  of  policies  issued  by  the  several  com-^ 
panics  will  find  that  the  reserve  equity — pretty  nearly  the 
entire  reserve,  for  that  matter — and  the  contingent  interest 
of  the  insured,  if  any,  in  dividends  are  made  the  foundation 
upon  which  is  reared  a  structure  of  numerous  options  avail- 
able in  the  settlement  of  lapsed  policies.  The  relative 
value  and  equity  of  these  options  in  any  particular  case 
cannot  be  determined  by  one  who  has  no  knowledge  of  the 
elementary  principles  of  life  insurance.  The  man  who 
decided  to  patronize  one  company  rather  than  another  be- 
cause the  surrender  values  of  the  former  were  based  upon 
"  the  reserve  with  ^  per  cent  interest,"  while  those  of  the 
latter  were  based  upon  "  the  reserve  with  4  per  cent  inter- 
est," made  a  mistake  due  to  his  ignorant  belief  that  the  4^ 
per  cent  reserve  was  the  larger. 

p'or  information  in  regard  to  surrender  values  actually 


i 


The  A  B   C  of  Life  Insurance,  5 1 

allowed,  the  reader  is  referred  to  the  published  literature  of 
the  companies.  .« 

The  most  elaborate  statutory  provisions  are  contained  in 
the  so-called  "Non-forfeiture  Law"  of  Massachusetts. 
This,  with  its  accompanying  tables,  constitutes  quite  a  for- 
midable document.  At  the  present  time  the  law  is  under 
criticism  by  the  Massachusetts  companies,  the  Insurance 
Commissioner  of  that  State  and  the  majority  of  American 
actuaries  for  the  alleged  reason  that  it  is  based  upon  an 
erroneous  and  inequitable  theory  of  surrender  values. 


52  The  A  B  C  of  Life  Insurance, 


CHAPTER  VIII. 

FLANS  OF  INSURANCE, 

The  words  "  insurance  "  and  *'  policy "  are  often  usee 
interchangeably,  thus :  "  An  insurance  of  five  thousanc] 
dollars,"  or  "  A  policy  of  five  thousand  dollars." 

Life  Policies.  • 

A  policy  payable  only  upon  the  death  of  the  insured  is 
known  as  a  life  policy.     When  the  premiums  are  paid  an- 
nually (or  in  semi-annual  or  quarterly  installments)  during ; 
the  lifetime  of  the  insured,  the  policy  is  called  an  ordinary, 
whole-life  policy. 

When  the  payments  are  to  be  completed  in  a  given  num- 
ber of  years,  the  term  limited-payment  life  policy  is  used. 
Or,  the   exact  term   is   mentioned,  as   "  ten-payment  Hfe," 
^*  fifteen-payment  life,"  etc.     The  payment  of  a  single  pre- 
mium constitutes  a  single-payment  life  policy.     Of  course,  \ 
all  limited-payment  premiums  are  higher  than  ordinary  pre-  ■ 
miums,  since  the  equivalent  of  payments  during  a  lifetime 
must  be  contained  in  the  limited  number  of  payments  made.  \ 
Consequently,  the  reserve  or  self-insurance  element  is  also 
larger. 

On  all  limited  payment  policies  it  is  customary  to  give 
paid-up  insurance  for  as  many  proportionate  parts  of  the 
original  amount  as  there  have  been  premiums  paid.  Thus  4 
premiums  paid  on  a  ten-payment  life  policy  of  $1000  would 
secure  paid-up  insurance  of  $400  payable  at  death ;  7  pre^ 
miums  paid  on  a  len-payment  endowment  of  $1000  at  6c 
would  secure  a  paid-up  endowment  of  $700  payable  at  60. 


I  UNIVERSITY   ) 
The  A  B  C  of  Lg%Jns^r,^nf^^^        53 

Joint-life  policies  are  contingent  upon  two  lives  (some- 
times more  than  two),  both  of  which  are  insured  under  one 
policy,  the  insurance  being  payable  to  !he  survivor  upon  the 
death  of  either.  The  premium  is  higher  than  that  upon  a 
single  life,  but  is  not  equal  to  the  sum  of  the  full  premiums 
on  both  lives.  Policies  of  this  form  are  not  in  favor  with 
American  companies  at  the  present  time.  Very  intricate 
calculations  are  involved  in  the  computation  of  joint-life 
premium  rates. 

Term  insurance  is  insurance  covering  a  specified  term. 
This  provides  for  payment  on  account  of  such  deaths  only 
as  occur  during  the  term.  The  example  on  page  23  is  an 
illustration  of  a  five-year,  term  insurance.  As  will  be  seen 
by  examination,  out  of  78,106  persons  living  at  age  40, 
only  3933  will  die  during  the  succeeding  five  years.  If  the 
term  of  the  insurance,  then,  is  limited  to  five  years,  the  pre- 
mium need  be  only  large  enough  to  provide  for  3933  deaths, 
while  a  whole-life  insurance  would  require  provision  for 
78,106  deaths.  The  term  premium  is  consequently  lower. 
When  the  policy  provides  for  insurance  for  a  specified  term, 
with  the  privilege  of  renewing  the  insurance  at  the  end  of 
that  term  for  another  similar  term,  upon  payment  of  a  pre- 
mium  adjusted  to  the  cost  of  each  successive  term,  it  is 
called  a  renewable  term  policv.  The  length  of  the  term  is 
indicated  by  such  nomenclature  as  "yearly  renewable  term,'* 
or  "  ten-year  renewable  term." 

Annuities. 
These  policies  provide  for  the  payment  of  a  certain 
yearly  sum  to  the  insured,  or  to  the  beneficiary  named  in 
the  policy,  during  the  life-time  of  the  annuitant  The 
premium  may  be  paid  in  one  payment,  or  in  annual  pay- 
ments for  a  given  number  of  years.     Its  amount  depends 


54  -^^  A  B   C  of  Life  Insurance, 

upon  the  relative  ages  of  the  insured  and  the  annuitant. 
Thus  if  A,  being  25  years  old,  insures  his  life  for  the  bene- 
fit of  his  mother,  60  years  old,  with  the  understanding  that 
the  insurance  is  to  be  an  annuity,  payable,  in  the  event  of 
his  death,  during  the  remainder  of  his  mother's  life,  the 
premium  would  be  very  small.  For  the  probability  is  chat 
A  will  survive  his  mother — in  which  case  the  company 
would  have  to  pay  nothing — or,  in  any  event,  that  he  will 
pay  a  considerable  number  of  premiums  to  the  company, 
while  his  mother  will  not  live  many  years  after  his  death 
to  receive  her  annuity.  On  the  contrary,  if  B,  the  insured, 
were  an  old  man,  and  his  daughter,  the  beneficiary,  were 
young,  the  chance  would  be  that  B  would  pay  comparatively 
few  premiums,  while  the  daughter  would  survive  him  many 
years  to  receive  her  annual  stipend.  In  such  a  case,  the 
premium  would  be  very  high.  Annuities,  while  quite  pop- 
ular in  Europe,  are  Httle  sought  after  in  this  country. 
Endowments. 
A  pure  endowment,  as  has  already  been  explained,  is  an 
agreement  to  pay  a  certain  sum  of  money  when  the  insured 
shall  have  reached  a  certain  age,  but  nothing  if  he  shall  die 
before  reaching  that  age.  Although  a  few  policies  of  this 
description  have  •  been  issued  in  this  country,  this  form, 
unmodified,  is  almost  never  used,  but  there  is  added  to  it 
an  agreement  to  pay  the  sum  insured  if  the  person  insured 
shall  die  before  reaching  the  specified  age.  Thus,  an  endow- 
ment assurance  of  $1000  at  60  means  that  the  company 
will  pay  $1000  if  the  insured  reaches  the  age  of  60,  or  upon 
his  death  at  any  time  before  that.  The  premium,  therefore, 
must  be  the  sum  of  two  premiums,  one  covering  the  insur- 
ance for  the  term,  and  the  other  providing  for  the  endow- 
ment at  the  end  of  the  term.  This  has  been  fully  ex- 
plained and  illustrated  in  Chapter  III. 


The  A  B   C  of  Life  Insurance.  55 

Endowments  are  sometimes  classified  by  the  age  which 
the  insured  must  attain  in  order  to  receive  the  amount  of 
the  poHcy;  thus,  an  "endowment  at  60,"  an  **  endowment 
at  70."  They  are  more  commonly  classified  by  the  term 
covered.  Thus,  an  endowment  on  a  hfe,  age  40,  payable 
^t  age  55,  would  be  called  a  *' 15 -year  endowment."  If 
a  premium  was  to  be  paid  each  year  during  this  term,  the 
policy  would  be  called  an  "  ordinary  15-year  endowment/' 
If,  however,  the  premiums  were  to  be  paid  in  10  years,  the 
policy  would  be  called  a  ^^ten-payment,  15-year  endow- 
ment." 

The  rate  of  premium  depends  upon  the  age  of  the  in- 
sured, the  length  of  the  endowment  term  and  the  number 
of  payments. 

Return-premium    Policies,    Instalment    Policies, 
Bonds,  Etc.,  Etc. 

The  preceding  policies,  three  only  in  number,  include  just 
about  everything,  in  principle^  which  is  possible  in  life  insur- 
ance. And  since  annuities  are  so  little  in  vogue  in  this 
country,  it  is  within  the  truth  to  say  that  the  life  policy  and 
the  endowment  are  the  principal  part  of  the  seventy- five  or 
more  differently  named  policies  which  are  to-day  offered  to 
the  public.  To  describe  any  considerable  number  of  these 
would  not  be  worth  the  space  which  it  would  require.  We 
mention  two  or  three. 

Some  policies,  either  life  or  endowment,  stipulate  that 
upon  the  death  of  the  insured,  within  a  specified  number  of 
years,  the  amount  of  the  premiums  paid  by  him  shall  be 
returned  in  addition  to  the  amount  named  in  the  policy. 
Other  policies  guarantee  the  payment  of  the  amount  of  the 
insurance  with  6  per  cent  interest  thereon.  Of  course,  in 
either  case  and  in    all  similar  cases,  the  addition   to  the 


56  The  A  B   C  of  Life  Insurance. 

amount  named  in  the  policy  is  just  so  much  additional 
insurance,  and  an  additional  premium  must  be,  and  always 
is,  charged  therefor. 

The  instalment  principle  has  been  widely  applied  to  both 
life  and  endowment  policies.  Thus  the  contract  of  a  whole- 
life  insurance  may  stipulate  that,  whenever  the  policy 
matures  as  a  death  claim,  the  amount  of  the  insurance  shall 
be  paid  in  a  specified  number  of  equal  annual  instalments. 
The  premium  for  this  would  be  less  than  for  the  same  form 
and  amount  of  insurance  payable  in  one  sum  at  the  death 
of  the  insured,  for  the  very  obvious  reason  that  the  risk  is 
not  at  any  time  the  full  aggregate  amount  of  the  instalments, 
but  only  the  present  value  of  those  instalments.  Thus  if  a 
policy  which  nominally  insures  for  ^20,000  stipulates  that 
that  amount  shall  be  paid  in  twenty  equal  annual  instal- 
ments, the  measure  of  the  risk  actually  assumed  by  the  com- 
pany under  that  policy  is  the  present  value  of  twenty  instal- 
ments of  ^1000  each,  the  first  payable  at  once,  the  second 
at  the  end  of  one  year,  the  third  at  the  end  of  two  years, 
and  so  on,  the  last  one  being  payable  at  the  end  of  nineteen 
years.  From  the  table  of  present  values,  page  76,  we  find 
this  to  be  $14,138,  or  a  little  more  than  seven- tenths  of  the 
nominal  insurance. 

The  foregoing  will  serve  as  examples.  A  most  admirable 
ingenuity  has  been  displayed  in  the  numerous  combinations 
of  life  and  endowment  insurance  with  the  return  of  all  pre- 
miums, or  a  portion  of  them,  with  the  payment  of  interest, 
at  different  rates  and  for  longer  or  shorter  terms,  and  with 
the  payment  of  the  principal  sum  insured  in  instalments 
covering  any  number  of  years  desired,  and  themselves  of 
uniform  or  varying  amounts.  In  the  keen  competition  for 
business  almost  every  possible  wish  or  necessity  of  the  in- 
suring public  has  been  met  by  one  or  another  of  the  com- 


The  A  B   C  of  Life  Insurance.  57 

panics.  The  nomenclature  by  which  these  different  forms 
are  known  is  equally  ingenious  and  sometimes  decidedly 
picturesque.  "* 

Tontines. 

In  1648,  Lorenzi  Tonti  organized  a  fund  in  Naples,  the 
conditions  of  which  were  as  follows :  Each  subscriber  paid 
a  certain  sum  of  money  into  the  fund.  The  total  fund  was 
invested,  and  the  interest  on  the  amount  of  each  subscrip- 
tion was  paid,  during  the  lifetime  of  the  subscriber,  to  such 
person  as  he  named.  At  the  death  of  a  subscriber  his  sub- 
scription was  forfeited  to  the  fund,  and  the  interest  thereon 
was  divided  among  the  subscribers,  who,  for  this  purpose, 
were  divided  into  classes  according  to  age.  At  the  death 
of  the  last  subscriber  the  entire  capital  subscribed  reverted 
to  the  crown. 

It  will  be  seen  that  this  is  the  converse  of  life  insurance, 
since  those  who  live  longest  receive  the  greatest  benefits. 
The  principle  of  forfeiture  on  the  part  of  those  who  die  and 
of  accumulation  for  those  who  live  is  known  as  the  "  Ton- 
tine "  principle,  and  is  perfectly  illustrated  in  the  pure  en- 
dowment, page  26.  That  application  of  this  principle  to 
life  and  endov/ment  insurance  policies  which  has  given  to 
such  policies,  as  a  cluss,  the  name  *'  Tontines,"  is  as  follows  : 

As  has  already  been  explained,  a  policyholder  who  has 
paid  premiums  for  several  years  and  then  given  up  his  in- 
surance, paying  no  further  premiums,  leaves  in  the  hands 
of  the  company  the  reserve  credited  to  his  policy,  and  also 
any  share  in  the  surplus  which  might  fairly  be  considered 
his,  but  which  has  not  been  actually  paid  to  him  in  the 
form  of  dividends.  Under  the  early  Tontine  practice  the 
entire  amount  of  this  reserve  and  of  this  surplus  was  credited 
by  the  company  to  the  other  policies  of  the  same  form  and 
class.     If  any  policy  became  a  death  claim  the  face  of  the 


58  The  A  B   C  of  Life  Insurance, 

policy  only  was  paid,  and  any  accrued  but  undivided  sur- 
plus thereunder  was  credited  in  like  manner.  Finally,  at 
the  end  of  a  specified  number  of  years,  known  as  the  Tontine 
period,  the  gains  from  these  sources  were  divided  among  the 
policies  of  the  same  form  and  class  which  then  remained  in 
force. 

This  practice  has  been  modified  so  that  in  many  cases 
the  Tontine  principle  is  now  applied,  after  the  policy  has 
been  in  force  three  years,  to  surplus  only,  the  retiring 
policyholder  receiving  an  equitable  consideration  in  paid-up 
insurance  (see  page  47)  for  his  reserve.  The  Tontine 
principle  is  applicable  to  any  form  of  policy  written  upon 
mutual  or  participating  premiums.  The  methods  of  ap- 
plication are  quite  numerous,  and  the  policies  are  variously 
designated  as  Semi-Tontine,  Free  Tontine,  Five,  Ten,  Fif- 
teen or  Twenty-year  Distribution  policies,  etc.  The  extent 
to  which  the  principle  is  applied  can  be  determined  only 
from  a  knowledge  of  the  terms  and  conditions  of  the  policy 
in  each  case.  The  different  companies  writing  this  kind  of 
policies  furnish  estimates  of  the  probable  results. 


The  A  B  C  of  Life  Insurance^  59 


CHAPTER  IX. 

CERTAIN  CONDITIONS  IN  POLICY 
CONTRACTS. 

Payments  of  Premiums, — Premiums  are  always  payable 
at  the  home  office  of  the  company,  but,  for  the  convenience 
of  the  policyholder,  are  allowed  to  be  paid  at  some  bank  or 
agency  near  him.  Prompt  payment  of  premiums  is  also  re- 
quired. In  actual  practice,  this  is  often  waived,  although 
there  would  seem  to  be  no  good  reason  why  the  insured 
should  not  pay  his  premiums  with  the  same  promptness 
which  he  expects  and  demands  from  the  company  in  the 
payment  of  its  losses. 

Residence  and  Occupation, — The  conditions  of  policies  in 
regard  to  these  matters  are  usually  exceedingly  liberal. ' 
Residents  in  notoriously  unhealthy  localities,  or  persons  en- 
gaged in  extra-hazardous  occupations,  would  not  be 
insured  by  any  company  at  the  usual  rates  of  premium. 
Policies  provide  that,  after  being  insured  at  the  usual  rate, 
the  policyholder  shall  not  reside  in  such  localities  or  engage 
in  such  occupations  without  first  obtaining  the  company's 
consent  and  paying  an  extra  premium  therefore.  The 
written  consent  of  the  company  is  called  a  "  permit." 

Use  of  Stimulants  and  Narcotics, — Some  policies  provide 
that  the  insured  shall  not  indulge  in  the  use  of  stimulants 
or  narcotics  to  such  an  extent  as  to  impair  his  health  or 
shorten  his  life. 

Suicide, — The  practice  of  different  companies  differs  as 
to  suicide.  Some  policies  provide  that  death  by  suicide, 
whether  the  insured  be  sane  or  insane,  shall  not  constitute 


6o  The  A  B  C  of  Life  Insurance, 

a  claim  against  the  company.  In  others,  death  by  suicide 
from  insanity  is  treated  as  the  natural  termination  of  the  dis- 
ease.    In  others,  no  reference  is  made  to  suicide. 

Non- Forfeiture, — As  already  stated,  every  company  now 
allows  some  equitable  return,  in  the  way  of  paid-up  or  ex-^ 
tended  insurance,  and  most  likely  in  cash,  for  the  reserve 
left  in  its  hands  by  the  lapse  of  a  policy.  Provision  for  this 
is  made  by  the  terms  of  the  poHcy,  and  consequently  the; 
reserve  equity  is  not  forfeited  by  failure  to  pay  a  stipulated 
premium. 

Incontestability. — Most  policies  provide  that,  subject  to 
the  conditions  of  the  policy  in  regard  to  residence,  occu- 
pation, and  the  payment  of  premiums,  the  insurance  shall  be 
incontestable  after  a  certain  number  of  years  (two  or  three). 
The  exact  phraseology  of  this  provision  differs  with  dif- 
ferent companies  and  policies.  The  general  effect  of  the  pro- 
vision, however  worded,  is  to  waive,  in  case  of  claim  against 
the  company  after  the  specified  term,  all  defenses  of  a  merely  • 
technical  nature,  or  such  as  might  be  based  upon  misstate- 
ments in  the  application,  made  without  fraudulent  intent. 
No  company  ought,  perhaps,  to  waive  its  right  to  contest  a 
fraud,  or  to  be  estopped  from  making  such  defense  if  good 
grounds  for  it  exist.  The  sensible  man  will  undoubtedly  admit 
that  there  is  no  more  reason  why  attempted  fraud  upon  an  ; 
insurance  company  should  not  be  resisted,  than  there  is  for 
non-resistance  to  any  other  form  of  fraud.  Attempts  of  this 
sort  sometimes  occur,  and  are  either  fought  out  in  the  courts 
or  settled  by  compromise  as  a  matter  of  expediency.  Resist- 
ance to  such  claims  is  always  creditable  to  a  company,  and 
should  have  the  support  of  agents  and  policyholders.  On 
the  other  hand,  the  fact  that  a  company  frequently  resists 
the  payment  of  claims  or  forces  compromises,  may  be  ac- 
cepted without  hesitation  as  proof  that  something  is  wrong 
in  the  management. 


The  A  B   C  of  Life  Insurance,  6i 

In  general,  there  are  two  things  which  should  be  said 
in  regard  to  the  conditions  of  the  later  .^policy  contracts. 

No  one  can  determine  what  are  all  the  conditions  of  any 
policy  by  an  examination  of  the  policy  only.  Every  con- 
tract of  insurance  consists  of  two  parts,  the  request  for  the 
insurance  known  as  the  '*  application/'  and  the  policy,  and 
these  two  are  in  legal  effect  one.  Consequently  any  stipu- 
lations or  conditions  recited  in  the  application  and  consented 
to  by  the  applicant,  as  witnessed  by  his  signature  thereto, 
are  as  much  a  part  of  the  contract  as  they  would  be  if 
printed  in  the  policy.  The  practice  of  the  companies  is  not 
uniform  in  this  respect,  and  in  one  case  the  majority  of  the 
conditions  appear  in  the  policy,  while  in  another  they  are  to 
be  found  in  the  application. 

The  general  tendency  in  late  years  has  been  toward 
fewer  conditions  and  restrictions,  and  greater  liberality. 
Certain  rights  and  obligations  of  both  parties  have  been 
definitely  established  in  practice  and  by  legal  decisions, 
while  others  have  been  made  matters  of  statutory  pro- 
vision. The  supposed  necessity  for  some  restrictions  has 
not  been  demonstrated  by  experience  to  be  a  real  necessity, 
and  in  the  case  of  some  others  where  it  cannot  fairly  be 
said  that  experience  has  demonstrated  anything,  thus  leav- 
ing the  matter  in  doubt,  the  companies  have  given  their 
patrons  the  benefit  of  the  doubt.  The  life  insurance 
manager  of  fifty  years  ago,  comparing  a  "latter  day" 
policy  with  one  of  his  own  lengthv,  verbose  and  minutely 
restricted  contracts,  would  be  more  than  likely  to  mistake 
the  former  for  a  promissory  note. 


62  2"he  A  B  C  of  Life  Insurance. 


CHAPTER  X. 

APPLICATIONS;  RISKS;   MEDICAL 
EXAMINERS. 

When  a  person  desires  insurance,  he  makes  application 
therefor  upon  printed  forms  furnished  by  the  company.  It 
is  intended  that  this  form,  when  properly  filled  out  and 
accompanied  by  the  report  of  the  Medical  Examiner,  shall 
furnish  the  company  with  information  which  will  enable  it 
to  decide  whether  or  not  the  applicant  is  a  desirable  risk. 
His  family  history  as  to  longevity,  existence  of  hereditary 
diseases,  etc. ;  his  own  personal  history  as  to  health  or 
disease,  residence,  occupation,  etc.;  his  present  residence 
and  occupation,  and,  last  but  not  least,  his  present  physical 
condition,  must  all  be  taken  into  the  account. 

It  is  here  that  the  Medical  Examiner  plays  a  most 
important  part.  It  is  his  duty  to  ascertain  the  present 
physical  condition  of  the  applicant,  and  from  the  results  of 
his  examination,  together  with  the  personal  and  family 
history  of  the  appHcant,  to  determine  the  probability  of  a 
long  or  short  life,  and  consequently  to  recommend  or  reject 
the  risk.  No  one  performs  a  more  important  duty  in 
connection  with  the  whole  business  of  life  insurance.  If 
Medical  Examiners  are  incompetent  or  careless,  the  best 
plans  of  insurance  and  the  ablest  management  will  end  in 
nothing  but  disaster.  The  fact  that  not  one  of  the  import- 
ant failures  of  life  insurance  companies  in  this  country  has 


The  A  B   C  of  Life  Insurance,  63 

been  due  primarily  to  excessive  mortality,  speaks  volumes 
for  the  skill  and  fidelity  of  the  MedicaUExaminers. 

It  might  appear,  at  first  sight,  that  a  rigid  medical  exam- 
ination should  result  in  a  large  saving  to  the  companies  by 
securing  for  them  an  exceedingly  row  rate  of  mortality.  It 
is  true  that  the  rate  is  generally  very  low  for  a  year  or  two 
among  newly  selected  risks,  but  the  effect  of  the  medical 
selection  disappears  more  rapidly  than  is  usually  supposed, 
and  but  a  comparatively  short  time  elapses  before  the  aver- 
age normal  rate  is  experienced.  The  very  low  cost  of 
insurance  in  assessment  organizations,  newly  organized,  is 
due  to  the  fact  that  the  risks  are  newly  selected,  but  it  is 
idle  to  expect  that  the  cost  can  be  kept  down  to  that  point 
by  the  infusion  of  "new  blood,"  or  by  any  other  process. 

If  impaired  or  doubtful  risks  were  not  summarily  rejected, 
the  selection  against  the  company,  already  alluded  to,  would 
assert  itself  at  the  very  outset.  The  better  class  of  lives 
would  drop  out,  and  the  company  would  find  itself  over- 
whelmed by  the  mortality  among  the  poorer  risks  remaining. 

Companies  have  been  formed  for  the  insurance  of  im- 
paired lives  at  an  adequate  rate  of  premium.  It  has  been 
found  very  difficult  to  determine  what  premiums  are  ade- 
quate, but  some  of  the  later  experiments  in  this  direction 
are  giving  promise  of  a  successful  solution  of  the  problem 
of  insuring  "sub-standard"  risks. 

If  sufficient  space  were  available,  it  would  be  interesting 
to  note  the  variations  between  the  standards  which  the  dif- 
ferent companies  make  in  the  matter  of  risks.  Probably 
it  would  be  correct  to  say  that,  in  a  very  general  way, 
all  Medical  Directors  agree  as  to  what  constitutes  a  desir- 
able, and  what  an  undesirable,  risk,  but  within  the  lines  of 
this  general  agreement  there  is  plenty  of  disagreement  on 
minor  points. 


64  The  A  B   C  of  Life  Insurance, 

Beside  its  presentation  of  the  applicant  as  a  risk,  the 
application  has  another  purpose  which  has  already  been 
mentioned — it  forms  the  basis  of  the  insurance  contract. 
The  applicant  asks  for  the  insurance,  declares  such  and  such 
things  to  be  true  in  regard  to  his  age,  place  of  birth,  per- 
sonal history,  present  residence,  occupation,  etc.,  and  agrees 
that  the  policy  may  be  issued  to  him  upon  certain  con- 
ditions. In  all  of  this  he  acts  as  agent  for  the  bene- 
ficiary named  in  the  policy  and  for  any  and  all  other 
persons  who  may  in  the  future  acquire  any  interest  in  the 
insurance.  It  is  not  necessary  to  suggest  that  an  applica- 
tion should  be  prepared  with  care,  and  that  the  applicant 
ought  to  acquaint  himself  with  all  its  terms  before  signing  it. 


/* 


The  A  B  C  of  Life  Insurance,  65 


CHAPTER  XI. 
ANNUAL   STATEMENTS;  RATIOS, 

The  laws  of  the  different  States  require  companies  to  file 
annually  statements  of  their  transactions  during  the  pre- 
ceding year,  and  of  their  financial  condition  at  the  close  of 
the  year.  The  forms  prescribed  by  the  Insurance  Depart- 
ments of  the  various  States  are  very  complete.  The  results 
in  detail  are  published  in  the  annual  reports  of  the  Depart- 
ments, and  are  frequently  accompanied  by  tables  of  per- 
centages and  ratios.  In  determining  the  value  of  these, 
some  knowledge  of  the  business  of  life  insurance,  and  more 
common  sense,  are  necessary.     For  instance : 

Percentage  of  expenses  to  income  is  not  always  a  reliable 
standard  by  which  to  judge  economy  of  management. 
Premiums  may  be  very  heavily  loaded  for  certain  forms  of 
insurance,  and  the  current  year's  expenses  may  exhaust  but 
a  small  part  of  that  loading.  Or  the  investment  part  of  the 
premiums  may  be  very  large,  and  the  premiums,  con- 
sequently, very  high.  The  amount  used  for  expenses 
would,  in  either  case,  constitute  but  a  comparatively  small 
percentage  of  the  gross  premiums.  On  the  other  hand,  the 
loading,  or  the  investment  part,  or  both,  of  premiums  may 
be  very  small,  in  which  case,  although  expenses  may  be 
kept  within  the  loading,  they  may  still  constitute  a  com- 
paratively large  percentage  of  the  premiums.     Consequently 


66  The  A  B  C  of  Life  Insurance. 

equal  economy  of  management  will  not  necessarily  result  in 
the  same,  or  even  nearly  the  same,  percentage  of  expense 
to  premium  income. 

The  ratio  of  assets  to  liabilities  is  of  little  consequence 
until  both  assets  and  liabilities  have  reached  respectable 
proportions.  If  A  has  but  one  dollar  in  the  world,  and 
owes  nothing,  the  ratio  of  his  assets  to  his  liabihties  is 
infinity.  If  B,  however,  is  worth  $200,000,  and  owes 
$100,000,  the  ratio  of  his  assets  to  his  HabiHties  is  only  two 
to  one.  Of  course,  after  a  company  has  been  in  business 
for  a  number  of  years  and  has  placed  a  large  amount  oi 
insurance  on  its  books,  the  percentage  of  its  assets  to  its 
liabilities  is  a  question  of  the  highest  importance. 

The  percentage  of  death  losses  to  the  mean  amount  in- 
sured during  the  year  affords  the  basis  of  a  fairly  close  esti- 
mate of  a  company's  mortality  experience.  But  an  exact 
determination  of  that  experience  cannot  be  made  without  a 
knowledge  of  the  ages  of  all  the  persons  insured,  and  conse- 
quently of  the  percentage  of  mortality  expected  by  the  com- 
pany and  provided  for  in  the  premium  charges. 

The  percentage  of  interest  {including  rents  and  profits  on 
sales  of  stocks^  bonds  and  real  estate)  to  mean  amount  of 
assets,  is  important.  If  premiums  are  calculated  and 
reserves  held  upon  a  basis  of  4  per  cent,  that  rate,  at  least, 
ought  actually  to  be  reaHzed. 

The  ratio  of  expenses  to  a^nount  of  new  business  secured 
may  be  of  much  or  little  importance,  depending  entirely 
upon  the  proportion  of  expense  fairly  chargeable  to  the 
securing  of  new  business,  as  well  as  upon  the  provision  for 
that  expense  made  in  the  premiums  charged. 

The  ratio  of  assets  to  amount  of  insurance  in  force 
is  of  Uttle  value,  the  main  question  always  being  whether 
present    accumulations,   together  with  future  premiums, 


^e 


The  A  B  C  of  Life  Insurance, 


67 


'e  sufficient  to  provide  for  future  claims.     If  future  pre 
miums  alone  are  sufficient,  the  question  of  present  accumu- 
lation is  of  less  consequence. 

And  so  on.  Persons  of  a  statistical  turn  of  mind  are 
constantly  furnishing  tables  of  ratios  and  percentages,  com- 
parative tables,  etc.,  etc.  Most  of  the  statistics  thus  compiled 
are  interesting,  many  of  them  are  valuable,  a  few  are  vital. 
Anyone  well  grounded  in  the  elementary  principles  of  life 
insurance,  and  fairly  familiar  with  the  practical  workings  of 
the  business,  can  decide  for  himself  to  which  class  belong 
such  statistics  as  come  under  his  observation. 


"Expectation"  Table. — Assured  Lives. 

(Constructed  from  the  American  Experience  Table  of  Mortality.) 


Age. 


10 
II 
12, 

13 
14, 

IS 
16 
17 
18, 

19 
20 
21 
22. 

23 
24 

25 

26 
27 
28 

29 
30 
31 
32 
33 
34 
35 
36 


Expecta- 
tion, 
Years. 


48.7 
48.1 

47-4 
46.8 
46.2 
455 
44-9 
44.2 

43-5 
42.9 
42.2 

41.5 
40.9 
40.2 
39  5 
38.8 
38.1 
37.4 
367 
36.0 

35  3 
34-6 
33  9 
332 
325 
31.8 
311 


Age. 


37... 
38--. 
39--- 
40... 
41... 
42... 

43- •• 
44... 

45... 
46... 
47... 
48... 
49--- 
50... 
51... 
52... 
53... 
54... 
55... 
56... 
57... 
58... 
59-.. 
60... 
61;.. 
62... 
63... 


Expecta- 
tion, 
Years. 


304 
29  6 
28.9 
28  2 

27.5 
26.7 
26.0 
25.3 
245 
23.8 
23.1 
22.4 
21.6 
20.9 
20.2 

19.'; 
18.8 
18.1 
17.4 
16.7 
16. 1 

154 
14.7 
14. 1 

135 
12.9 
12.3 


Age. 


64 

65 
66 
67 
68 
69 
70 

71 
72, 

73 

74 
75 
76 

77 
78 

80 
81 
82 
83 
84 
85 
86, 

87 
88 

89 
90 


Expecta- 
tion, 
Years. 


2  5 

2   2 

1.9 

1-7 
1.4 


68  The  A  B  C  of  Life  Insurance. 

American  Experience  Table  of  Mortality. 


c 

bXI 

u 

G  O 

B 

0,; 

.^^ 

H 

.2  h-^  bo 

^1 

o.S 

r 

^  W) 

0 

Ho^ 

M 

;z; 

5-PQ 

ICO.OCO 

749 

.007490 

99.251 

746 

007516 

98.505 

743 

•037543 

97,762 

740 

.007569 

97,022 

737 

.007596 

96,285 

735 

.007634 

95.550 

732 

.007661 

94,818 

729 

.007688 

94.089 

727 

.007727 

93,362 

725 

.007765 

92,637 

723 

.007805 

91,914 

722 

.007855 

91.192 

721 

.007906 

90471 

720 

•007958 

89.751 

719 

.008011 

89  032 

718 

.008065 

88314 

718 

.0  8130 

87596 

718 

.008197 

86,878 

718 

.008264 

86,160 

719 

.008345 

85,441 

720 

.0  8427 

84.721 

721 

.008510 

84.000 

723 

.008607 

83.277 

726 

.008718 

82.551 

729 

.008831 

81,822 

732 

.008946 

81,090 

737 

.009089 

80.353 

742 

.OC9234 

79.611 

749 

.009408 

78,862 

756 

.009586 

78  106 

765 

.009794 

77.341 

774 

.010008 

76.567 

785 

.010252 

75.782 

797 

.010517 

74.985 

812 

.010829 

74.173 

828 

.011163 

73.345 

848 

.011562 

72497 

870 

.012000 

71,627 

896 

.012509 

70,731 

927 

.013106 

69,804 

962 

.013781 

68,842 

1,001 

.014541 

67,841 

1,044 

.015389 

Age. 


53 
54 
55. 
56^ 
57- 
58. 
59- 
60, 
61. 
62. 

63. 
64, 

65 
66, 

67. 
68. 
69. 
70 
71 
72 

73  ■ 
74 
75 
76 
77 
78 
79 
80 
81 
82. 
83 
84 
85 
86 

87 
88 

89 
90 
91 
92 
93 
94 
95 


l4 

hfl 

^  * 

C 

l> 

c  0 

^u 

.t  wi 

^f> 

hJ.S 

•>•> 

0  a 

Pi 

^•^ 

0 

PQ 

^ 

66.797 

i,c9i 

65.706 

1. 143 

64563 

1,199 

63.364 

1,260 

62,104 

1325 

60.779 

1.394 

59.385 

1,468 

57,917 

1,546 

56.371 

1,628 

54.743 

1. 713 

53.030 

1.800 

51.230 

1,889 

49341 

1,980 

47.361 

2,070 

45.291 

2,158 

43.133 

2243 

40,8qO 

2  321 

38,569 

2,391 

36,178 

2,448 

33.730 

2,487 

3^243 

2505 

28,738 

2.501 

C6237 

2,476 

23,761 

2431 

21,330 

2369 

i8,q6i 

2  291 

16,670 

2,196 

14.474 

2,091 

12,383 

1,964 

10,419 

I  816 

8603 

1,648 

6.955 

1,470 

5,485 

1,292 

4,193 

1,114 

3.079 

933 

2,146 

744 

1,402 

555 

847 

385 

462 

246 

216 

137 

79 

58 

21 

18 

3 

3 

The  A  B   C  of  Life  Insurance, 


69 


Net  Premiums  for  a  Whole- Life  Insurance  of  $1000. 

Based  upon  the  American  Experience  Table  of  Mortality,  with  4  per  ceilt  interest. 


Age. 


20 
21 
22 

23 
24 

25 
26 

27 
28 

29 
30 
31 
32 
33 
34 

^i 

36. 

38 
39 
40 
41, 
42 
43 
44. 

45' 
46 

47 
48, 

49 
SO. 
51 

52. 
S3 
S4. 

56. 
57 
58 
59 
60 
61 
62 

64 
65 


Single  Pre- 
miums 
which  are 
also  Net 
Reserves 
on  Paid-up 
Policies, 


$247.77 
251-85 
256.08 
260.47 
265.04 
269.79 
27474 
279.87 
285  21 
29075 
296.51 
302  50 
308  71 
315  17 
321.86 
328.81 
33602 
34850 
35124 
359-27 
367-57 
376.17 
385.06 
394-25 
403-75 
41355 
423  66 
434.06 
444.76 

455-74 
466.99 
47848 
490.21 
502.15 
514.31 
526.65 

539.15 
551  81 
564.59 
577.48 
590.46 

603.49 
616.56 
629.63 
642.69 
655.70 


Annual 

Premiums 

During 

Life. 


$12  67 

^2.95 
13.24 

13-54 
13-87 
14.21 

14.57 
14-95 
15-35 
1577 

16  21 
f6.68 

17  18 
17.70 
18.25 
18.84 
19.46 
20.12 
20  82 

21.57 
22.35 
23.19 
24  08 
2503 
26.04 
27.12 
28  27 
29.50 
30. 8  E 
32.21 
3370 
3529 
36.98 

3879 
40.73 
42.79 
45.00 

47-35 
49.87 

5257 
55-45 
58.54 
6t  84 

65  39 
69  18 
7325 


Annual 

Premiums 

for 

Twenty 

Years. 


$18.73 
19.05 
19-38 
19.72 
20.08 
20.46 
20.85 
21.26 
21.68 
22.13 

22.59 
23.08 

23.59 
24.12 

24-67 
25.26 
2587 
26.51 
27.18 
27.88 
28.68 
29.41 
30.24 
31  II 
32.03 
33.00 
3404 
35.14 
3630 
37.55 
38.86 
4027 
41.76 
43.36 
4506 
46.88 
48.84 
50.93 
53-17 
55-59 
58.18 
60.98 

63-99 
67.24 

7075 
74  54 


Annual 

Premiums 

for 

Fifteen 

Years. 


SP22.53 
22.91 
23.30 
23.71 
24.14 
24.58 
25.05 
25-53 
26.03 
26.56 
27.10 
27.67 
28  27 
28.89 

29-53 
30.20 
30.91 
3164 
32-41 
33-21 
34.05 
34-93 
35-85 
36.82 

37.83 
38.90 
40.02 
41.21 
42.45 
43.76 
45  14 
46.60 

48-13 
49.76 

51.47 
53-29 
55.21 
57.26 

59-44 
61.76 
64.25 
66.90 

69.74 
72.79 
76.07 
7959 


70 


The  A  B  C  of  Life  Insurance. 


Annual    Premiums— Analysis   of   First   Year's    Premium, 
Different  Ages,  $icxx)  Whole-Life  Insurance. 
Participating  Rate. 


AGE. 


Net  Premiums,  American  Ex- 
perience Table  of  Mortality, 
with  4  Per  Cent  Interest. 


Portion 
for  Death 
Claims. 


$7-71 
7.76 
7.Z2, 
7.88 
7.96 
803 
8.11 
8.20 
830 
8.40 
8.51 
8.64 

877 
8-93 

9  TO 

9.29 
9.49 
9.71 

9-95 
10.24 

10.5s 
10  92 
11.32 

11.79 
12.34 
12.97 
13.67 
1445 
15.33 
16  30 

17-38 
18.60 

1993 
21.40 
23.10 
24.85 


Portion 

for 
Reserve. 


$650 
6.81 
7- 13 
7-47 
7.8r 
8.18 

8.57 
8.98 
9.40 
986 

IO-33 
10.82 

11-35 
11.89 
12.47 
1306 
13.70 
1437 
15.08 
15.80 
16.57 
17.35 
18.18 
19  02 
1987 
2073 
21.62 

22.53 
23.46 

24-43 
25.41 
26.40 
27.42 
28.67 

2953 
30.60 


Total 

Net 
Premiums 


$14.21 
1457 
149s 
15-35 
1577 

16  21 
16.68 

17  18 
17.70 
18.25 
18.84 
19.46 
20.12 
20.82 
21.57 
22.35 
23.19 
24  08 
2503 
26.04 
27.12 
28.27 
2950 
30.81 
32.21 
3370 
3529 
36.98 
3879 
40.73 
42.79 
4500 

47.3s 
49.87 

52.57 
55-45 


Loading. 


$5-63 
583 
5.98 
6.13 
6.30 
649 
6.67 
6.87 
7.08 
7-30 
7-54 
7  79 
8.05 

8.33 

8.62 

8.9s 

9.28 

9.64 

10.02 

10.42 

10.85 

IT. 31 
11.80 
12.32 

12  88 
1348 

14  IT 
14.80 
15.52 
16.29 
17  12 
18.00 
18.94 

1995 
21.03 
22.18 


See  Explanatory  Notes  on  Page  77. 


The  A  B  C  of  Life  Insurance. 


71 


^^K       Actuaries'  or  Combined  Experience  Table 

^^  OF   MORTALfTY. 

The  following  table  was  prepared  by  a  committee  of 
eminent  actuaries  on  the  data  afforded  by  the  combined 
experience  of  seventeen  of  the  principal  life  insurance  offices 
in  England.  It  was  deduced  from  62,537  assurances.  Some 
of  the  objections  advanced  against  it  are  that  certain  lives 
have  been  more  than  once  assured,  have  appeared  twice  or 
oftener  as  elements  of  the  calculation,  and  that  the  data  for 
the  older  ages  were  insufficient.  The  average  duration  of  all 
the  policies  was  a  little  less  than  eight  and  a  half  years.  The 
later  Actuaries'  or  H.  M.  (healthy  males)  Table  is  now  more 
generally  used  in  England.  The  American  Experience  Table 
furnishes  a  better  standard  than  either  for  American  lives. 


Age. 

|i 

3 

Ratio  of  Deaths 

During  the  Year  to 

Number  Living  at  the 

Beginning  of  the  Year. 

Age. 

:>o 

►J  bJO 

is 

I 

3 

3 

10 

IT 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

100,000 

99.324 
98,650 
97.978 
97.307 

96,636 
95.965 
95.293 
94,620 

93.945 

93.268 
92,588 

91.905 
91,219 
90,529 

676 

674 
672 
671 
671 

671 
672 
673 
675 
677 

680 
683 

686 

S^ 
694 

.006760 

.006786 
.006812 
.006848 
.C06896 

.006944 
.007003 
.007062 
.007134 
.007206 

.007291 
.007377 
.007464 
.007564 
.007666 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

p::::::: 
P::::::: 

39 

89.835 
89.137 

^7,726 
87,012 

86,292 
85.565 
84.831 
84,089 

83.339 

82,581 
81,814 
81,038 
80.253 
79.458 

698 

703 
708 

714 
720 

72.7 

734 
742 
750 
758 

767 
776 
785 

Q   S  ** 

fi3^ 


.007770 
.007887 
.008006 
.008139 
.008275 

.008425 
.008578 
.C08747 
.008919 
.009095 

.009288 
.009485 
.009687 
.009906 
.010131 


72 


The  A  B  C  of  Life  Insurance, 


Actuaries'  or  Combined  Experience  Table 
OF  Mortality. 

{Continued  front  preceding  ^age^ 


•r  5  ^ 

1)  4)   « 

5  « 


78,653 
77.838 
77,012 
76.173 
75.316 

74.435 
73.526 
72,582 
71,601 
70.580 

69.517 
68,409 
67.253 
66,046 
64,785 

63,469 
62,094 
60658 
59.161 
57.600 

55.973 

54.275 
52,505 
50,661 

48,744 

46,754 
44.693 
42.565 
40.374 
38,128 


^2 


815 
826 

839 
857 
881 

909 

944 

981 

1,021 

1,063 

1,108 
1. 156 
1,207 
1,261 
1,316 

1.375 
1.436 
1.497 
1,561 
1,627 

1,698 
1,770 
1,844 

1.917 
1,990 

2,061 
2,128 
2,191 
2,246 
2,291 


•5  rt  rt*^ 


.0 10362 
.010612 
.010894 
.011251 
.011697 

.012212 
.012839 

.013517 

.014260 
.015061 

•OI593Q 
.0^6898 
.017947 
.019093 
.020313 

.021664 
.023126 
.024679 
.026386 
.028247 

.030336 

.032612 
.035120 
.037840 
.040826 

.044082 
.047614 

.051474 
.055630 

.060087 


70 

71 
72 

73 
74 

75 
1^ 
77 
78 
79 

80 
8i 
82 
83 
84 

85 

86 

87 
88 

89 

90 

9C 
92 

93 
94 

96 
97 
98 
99 


4>  U 

,£i   OS 

i!< 

t> 

«.• 

^^ 

^2 

'l> 

1^ 

%-i 

9 

^^ 

55 

35.837 

2.327 

33.510 

2,351 

31.159 

2,362 

28,797 

2.358 

20,439 

2.339 

24,100 

2,303 

21,797 

2,249 

19.548 

2,179 

17.369 

2,092 

^S^277 

1,987 

13.290 

1,866 

11,424 

1.730 

9.^94 

1,582 

8,112 

1.427 

6,685 

1,268 

5.417 

1,111 

4.306 

958 

3.348 

81E 

2,537 

673 

1,864 

545 

1.3^9 

427 

892 

322 

570 

231 

339 

155 

184 

95 

89 

52 

37 

24 

13 

9 

4 

3 

I 

I 

The  A  B   C  of  Life  Insurance, 


73 


Net  Premiums  for  a  Whole-Life  Insurance  of  $1000. 

Based  upon  the  Combined  Experience  Table  of  Mortality,  with  4  percent  interest. 


20 
21 
22 

23 
24 
25 
26 
27 
28 
29 
30 
31 
32 

33 
34 
35 
36. 

37 
38. 
39 
40. 
41. 
42. 

43- 
44. 

45- 
46. 

48. 
49. 
50- 
51- 
52. 
53- 
54. 
55. 
56. 
57. 
58. 
59. 
60. 
61. 
62. 
63. 
64, 
65. 


$251.88 
256.57 
261.38 
266.34 
271.49 
276.80 
282.29 
287.98 
293.84 
299.91 
306.14 
312.61 

319-31 
326.15 
33327 
340.61 
348.16 
356.00 
364.08 
372.42 
381.04 
38996 
399- 18 
408.69 
418.49 

42857 
438.84 

449-34 
460.04 
470.88 
481.92 
493" 
504.46 
515-97 
527-59 
539-32 
551-15 
563-12 

57515 
587.27 
599-43 
611.62 
62385 
636  00 
648.11 
660.19 


$12.95 

'  13.27 

13.61 

13.96 

M-33 
14.72 

15  13 

1556 

16. OT 
16.48 
16.97 

1749 
18.04 
18.62 
19.23 
19.87 
20.54 
21.26 
22  02 
22.82 
23.68 
2459 

25-55 
26.58 
27.68 
28.85 
30.08 
31-39 
32.77 
3423 
35-78 
37.42 
39-15 
41.00 

42.95 
4503 
47-23 
4957 
5207 
5472 
5756 
60.57 
6378 
67.20 
70.84 
74.72 


Annual 

Annual 

Premiums 

Premiums 

for 

,        for 

Twenty 

Fifteen 

Years. 

Years. 

$19.00 

$22.86 

'     19-37 

23.29 

1976 

23-75 

20.15 

24.22 

20.57 

2471 

21.00 

25  21 

21.44 

25-74 

21.90 

26.28 

2238 

26.84 

22.88 

27-43 

23-39 

28.03 

2393 

28.65 

24.49 

29.30 

25.07 

29-97 

25.68 

30.67 

26.32 

31.40 

26.98 

32.15 

27.67 

32.94 

28.40 

33-76 

29.17 

3462 

29.98 

35-53 

30.83 

3647 

31-74 

37-47 

32.69 

3852 

3371 

39-63 

34-77 

40.78 

3590 

41.99 

37.08 

^53-25 

38.32 

44.57 

39-63 

45-95 

41  02 

47-38 

42.48 

48.89 

4402 

5046 

45-66 

52.12 

47-39 

53.86 

4924 

5569 

51.20 

57.63 

5329 

59.67 

55  53 

61.84 

57-92 

64.15 

60.49 

6660 

63.24 

69.21 

66.18 

71.99 

69-33 

74.96 

72.71 

78.12 

7634 

81.50 

74 


The  A  B  C  of  Life  Insurance, 


Ordinary,  Continued-Payment,  Whole-Life. 

net  value,  or  reserve  of  a  premium-paying  policy  of 

$1000,  at  the  end  of  various  years,  actuaries* 

table,  4  per  cent 


ist 
Year. 


7.60 
7.91 
8.24 
8.58 
8.93 

9-31 
970 

lO.II 

10.54 
11.00 

II  48 
11.99 

12.55 
13  12 

1374 

14.41 
15  12 
15.85 
1659 
17.30 

18.01 
18.69 

1939 
20.10 
20.86 

21.62 
22.39 
23.19 
24.00 
24.85 

25.72 
26.61 
27.56 
28.52 
29.50 
3045 


ad 
Year. 


15-45 
16.09 

1675 
17.43 
18.16 

18.91 
19.70 
2054 
21  42 
22.35 

23.33 
24.39 
2551 
26.69 
27.96 

29.31 

30.73 
32.18 

33-59 
34.99 

3636 
37.71 
39.10 

40.54 
42.02 

43-52 
4506 
46.63 
48.26 
49.94 

51.65 
53.43 
55-29 
57.18 
5905 
60.90 


3d 

4th 

5th 

6th 

7th 

Year. 

Year. 

Year. 

Year. 

Year. 

$ 

$ 

$ 

$ 

$ 

2356 

31.94 

40.58 

49-51 

58.73 

24.52 

3324 

42.24 

51-52 

61. II 

2553 

34.60 

4396 

53.62 

6359 

26.58 

36.02 

4576 

5581 

6620 

27.68 

37.50 

47.64 

58.12 

68.93 

28.83 

3906 

49.63 

60.54 

71.80 

30.03 

40.70 

51  71 

63.08 

74.84 

31.31 

42-43 

53.91 

65.78 

7804 

32.65 

44-25 

56.25 

68.63 

81.43 

34.07 

46.20 

58.71 

71.65 

85.03 

35.59 

48.25 

61.34 

74-86 

88.84 

37.19 

50.43 

64.11 

78.26 

92.87 

38.90 

52.75 

67.08 

81.87 

97.09 

40.72 

55-22 

70.20 

85.62 

101.43 

4^.65 

57.83 

73.46 

8948 

105.88 

44.70 

60.55 

76.79 

93-42 

110.36 

46  81 

6329 

80.16 

97-35 

114.85 

4891 

66.04 

83-49 

101.26 

119.32 

5100 

68.73 

8678 

105.13 

123  80 

53.02 

71.38 

90.04 

109.02 

128.28 

55.04 

7403 

.93  34 

11294 

13280 

57.05 

76.72 

96.67 

116.90 

137.38 

59.14 

79.47 

100.09 

120.95 

142.05 

6128 

82.30 

103-57 

125.09 

146.83 

63.47 

85.19 

107.14 

129.34 

151-73 

65.70 

88.13 

110.79 

133.67 

15672 

67.98 

91.14 

114-53 

138.09 

161.84 

70.33 

94-24 

118.34 

142.64 

167.09 

72.74 

97.42 

122  29 

147.32 

172.47 

75.22 

100.70 

12635 

152.12 

177-93 

77.78 

10408 

130.51 

156.98 

183.46 

80.42 

107.55 

134-72 

161.90 

189.01 

83-15 

III. 07 

138-99 

166.84 

194-59 

85.88 

114  59 

14323 

171.76 

200.14 

88.60 

118  08 

147  46 

176.66 

20563 

91.28 

121  54 

151-63 

181.49 

2ir.02 

See  Explanatory  Notes  on  Page  77. 


The  A  B  C  of  Life  Insurance.  75 

Ordinary,  Continued-Payment,  Whole-Life. 

net  value,  or  reserve  of  a  ^remium-paying  policy  of 

$1000,  at  the  end  of  various  years,  actuaries' 

table,  4  per  cent. 

( Continued  from  preceding  page. ) 


gth 
Year. 


$ 
7806 

8452 
87.99 
91.64 

95-48 

99-53 
103.82 
108.36 
11315 

118. 16 

12335 
128.69 
134.10 
139.60 

145-14 
150.73 
156.33 
161.94 
167.56 

17324 
179.12 
184.90 
190.90 
197.06 

203.34 
209.76 
216.27 
222.86 
229.51 

236. 19 
242.87 

249-54 
256.13 
262  63 
269.02 


loth 
Year. 


$ 
88.20 
91.76 
95-50 
99-43 
103.56 

107.91 
112.51 

117-37 
122.50 
127.86 

133-41 
139-13 
144.97 
150  89 
15689 

162.97 
169.09 
175.22 
181.37 
187.54 

193-79 
2C0.13 
206.59 
213.19 
21995 

226.84 
233.82 
240.88 
248.00 
255.18 

262.35 
269.52 
276.63 
283.65 
290.58 
297.42 


iSth 
Year. 


$ 
144.12 
149.99 
156.17 
162.65 
169.41 

176.42 

183.65 
191.06 
198.65 
206.39 

214.30 
222.36 

230.54 
238.83 
247.22 

255-70 
264.25 
272.83 
281.47 
290. 19 

299.01 
307.89 
316.86 
325-89 
33498 

344-07 
353-18 
362.24 
37^-25 
380.21 

389.11 
397.92 
406.65 
415.26 

423-74 
432.09 


20th 
Year. 


$ 
209.84 
218.13 
226.62 

23531 
244.20 

25329 
262.57 
272,02 
281.64 
291.42 

301-35 
311.42 
321.60 
331  91 
342.33 

35284 
363-37 
37390 
38439 
394.86 

40530 
415-71 
426.07 

43637 
446.62 

45679 
466.88 
476.87 
48676 
496-55 

506.21 

515.79 
525-16 
534-43 
543.52 
552.49 


25th 
Year. 


$ 
283  60 
29372 
30403 
314-51 
325.18 

336.02 
347.02 
358-17 
36949 
380.94 

392.53 
404.18 

41589 
427.60 

439-31 

450.97 
462.54 

47398 
485-29 
496.45 

507-49 
518.41 
52923 
53992 
55049 

560.91 
571  20 
581.36 
591-36 
601.20 

610  89 
620.47 
630.03 
639  68 
649.52 
659.75 


^oth 
Year. 


$ 
362.97 
374.60 
386.39 
398.34 
410.44 

422  68 
434.90 
447.38 
459.80 
472.23 

484.64 
497.00 
50927 
52142 
533  44 

545-32 
55702 
568.53 
57985 
59097 

601  90 
612  65 
623.26 
633.69 
64393 

654.00 
663.94 
673.82 
68374 
693-81 

70415 
714-83 
72588 
737.37 
749.24 
761.42 


35th 
iTear. 


446.  IT 
458.86 
471.67 
48452 
497.38 

510.21 
52301 

535-72 
548.34 
560.83 

57320 
58542 
597-47 
609.34 
621  01 

63247 
644.11 

654-71 
665.47 

67599 

686.30 
696.43 
706.46 
716.50 
726.61 

73693 
747-48 
758.32 
769.48 
780.92 

79251 
804  24 
815.99 
827.41 
838.15 
847-87 


See  Explanatory  Notes  on  Page  77. 


76 


The  A  B  C  of  Life  Insurance. 


Present  Value  of  $i   Due  at  End   of  Year  in  from 
One  to  Forty  Years  from  the  Present  Time. 


No.  OF  Years. 


3 

4 

c 

6 

7 
8 

9 

lO 

TI 
12 
13 

14 
15 
i6 

17 
i8 

19 

20 

21 
22 
23 
24 
25 
26 

27 

28 
29 

30 

31 
32 

33 
34 
35 
36 
37 
38 
39 
40 


Four  Per 
Cent. 


,961538 
924556 
888996 
854804 
821927 
790315 
759918 
730690 
702587 
675564 

649581 
624597 
600574 
577475 
555265 
533908 
513373 
493628 
474642 
456387 

438834 
421955 
405726 
3901 2 I 

3751 17 
360689 

346817 
333477 
320651 
308319 

296460 
285058 
274094 
263552 

253415 
243669 
234297 
225285 
216621 
208289 


Four  and 
One-Half 
Per  Cent. 


956938 
915730 
876297 
838561 
802451 
767896 
734828 
703185 
672904 
643928 

616199 
589664 
564272 

539973 
516720 

494469 
473176 
452800 
433302 
414643 

396787 
379701 
363350 
347703 
332731 
318402 
304691 
291571 
279015 
267000 

255502 
244500 

233971 
223896 
214254 

164525 
196199 
877501 
179665 
I 71929 


Five  Per 
Cent. 


952381 
907029 
863838 
822702 
783526 
746215 
710681 
676839 
644609 
613913 

584679 
556837 
530321 
505068 
481017 
458112 
436297 
415521 
395734 
376889 

358942 
341850 
325571 
310068 

295303 
281241 

267848 

255094 
242946 

231377 

220359 
209866 
199873 

190355 
181290 
135282 
164436 
156605 
149148 
142046 


Six  Per 
Cent. 


The  A  B  C  of  Life  Insurance.  77 

EXP  LAN  A  TOR*y  NO  TES. 


Pages  74  and  75. — Reserves  are  calculated  upon  the  basis  qjnet  pre-, 
miums.     The  amount  of  loading,  added  to  the  net  premium  to  make  the'^ 
gross  premium,  does  not  aftect  the  reserve.     Upon  the  same  kind  of  a 
policy,  issued  at  the  same  age  and  with  the  same  number  of  premiums 
paid,  the  reserve  would  be  the  same,  no  matter  what  amount  of  annual 
premium  might  be  charged  for  the  insurance. 

Under  premium-paying  policies,  the  amount  of  the  reserve  depends 
upon  the  age  of  the  insured  at  the  time  the  policy  was  issued,  and 
the  number  of  premiums  paid.  Under  paid-up  insurance,  the  amount  of 
the  reserve  depends  entirely  upon  the  age  of  the  insured  at  the  date 
for  which  the  reserve  is  computed. 

The  reserves  given  are  based  upon  the  Actuaries'  Table  of  Mortality, 
with  4  per  cent  interest.  See  pages  33  and  34.  For  the  sake  of  exactness 
it  should  be  said  that,  while  these  reserves  are  for  the  most  part  greater 
than  those  based  upon  the  American  Experience  Table,  with  4^  per  cent 
interest,  the  latter  are  the  greater  at  the  very  highest  ages.  The  reason 
for  this  is  that  according  to  the  American  Table  the  term  of  life  ends  with 
age  95,  while  according  to  the  Actuaries'  it  continues  to  age  100. 


Page  73. — The  net  single  premiums  given  are  also  the  net  values 
or  reserves  of  a  paid-up  pohcy  of  $1000  at  the  different  ages.  To  esti- 
mate pretty  nearly  the  amount  of  paid-up  insurance  which  a  company 
would  allow  for  the  surrender  of  an  ordinary  whole  life  policy  with  pre- 
miums payable  annually,  ascertain  the  reserve  on  that  policy  according  to 
the  table  of  reserves  on  pages  74  and  75,  and  divide  90  per  cent  of  it  by 
the  single  premium  given  for  the  age  actually  attained  by  the  policyholder 
at  the  time  of  surrendering  his  original  pohcy  for  paid-up  insurance. 


Page  70.— This  table  shows  the  component  parts  of  both  the  net  and  the 
gross  (or  office)  premiums  at  different  ages,  for  an  insurance  of  $1000, 
payable  at  death.  This  analysis,  however,  is  correct  for  ihejftrst  year  of 
the  insurance  at  each  age  only.  Each  subsequent  year  the  portion  of  the 
premium  used  for  death  claims  is  greater,  and  the  portion  used  for  reserve 
is  smaller  than  these  respective  portions  for  the  first  year.  The  accumu- 
lated reserve  incre^ises  each  year  by  the  addition  of  that  year's  reserve 
portion  of  the  premium  and  of  interest,  as  is  shown  in  table  on  page  36. 
The  "loading"  remains  the  same  theoretically  for  each  year  of  the  insur- 
ance, although  the  amount  actually  collected  by  the  company  will  vary 
wirh  the  amount  of  dividend  allowed  on  that  account. 


WH/T  IS  THOUGHT  OF  THE/  B  C  OF  LIFE  INSURAp. 


OPINIONS    OF    EXPERTS. 

COL.  J  A  COB  L»  GREENE,  President  Connecticut  Mutual  Life  Insurance 
Company y  Hartford^  Conn. 
*'  I  find  it,  as  I  expected  from  its  authorship,  to  be  a  clear  and  concise  statement 
of  the  matters  therein  treated,  and  I  should  think  that  it  would  be  useful  for  the 
purpose  which  I  presume  it  is  intended  to  serve — the  instruction  of  new  agents. 
It  has  the  advantage  of  some  other  elementary  works  which  I  have  seen,  of  much 
greater  brevity." 

HON.  JAMES  G.  BATTERSON^  President  Travelers  Insurance  Company., 
Hartford^  Conn. 
"  It  is  a  very  plain  and  intelligent  statement  of  the  case.  I  am  glad  that  you 
have  kept  out  of  the  actuarial  field.  The  various  propositions  stated  arithmetic^ 
ally  can  be  easily  comprehended.  Clear  away  mysteries  from  life  insurance  and 
the  people  will  take  it.     You  have  done  a  good  and  useful  work." 


DAVID  PARKS  FACKLER,  Consulting  Actuary,  New  York. 

*'  I  have  endeavored  to  read  through  your  little  treatise  with  the  attention  due 

to  its  compact  and  masterly  style For  the  purpose  it  has  in  view  it 

seems  to  excel  anything  I  have  seen,  and  I  hope  it  will  have  the  wide  circulation 
it  merits."  

SHEPPARD  HOMANS,  Consulting  Actuary,  New  York, 

"  The  '  A  B  C '  is  the  modest  title  of  a  manual  of  life  insurance  which  should 
•be  studied  by  every  canvassing  agent.  It  is  not  ©nly  full  of  valuable  information 
relating  to  the  fundamental  principles  of  the  business,  couched  in  language  free 
from  algebraic  formulas,  but  it  contains  information  concerning  the  practicdl 
application  of  these  principles  which  is  of  great  value  to  the  student," 


OPINIONS    OF    PRACTICAL    FIELD    MEN. 

SUDLOW  &>  MARSH,  Indianapolis,  Ind. 

**  We  have  looked  it  over  very  carefully,  and  are  very  glad  to  say  that  we  think 
it  will  subserve  a  most  desirable  purpose  in  the  education  of  agents.  Further,  the 
tables  contained  therein  are  very  simple,  decidedly  good,  and  will  prove  of  great 
assistance  in  soliciting  business.     It  meets  our  hearty  commendation." 


R.  L.  DOUGLAS,  Philadelphia,  Pa, 

*'  It  is  an  exceedingly  instructive  and  enjoyable  production.  What  a  contrast 
between  to-day  and  twenty  years  ago  !  Then,  and  even  at  a  much  later  period,  it 
was  generally  supposed  that  the  subject  of  life  insurance  was  a  mystery  beyond 
the  reach  of  ordmary  intellects.  Mr.  Elizur  Wright  and  Mr.  Sheppard  Homans 
punctured  that  illusion.  This  book  of  yours  is  another  long  stride  in  advance 
You  take  the  bed  rock  and  build  from  it  " 


The  A  B  C  of  Life  Insurance,  79 

WHAT  IS  THOUGHT  OF  THE  A  B  C  OF  LIFE  INSDRANCE.-c.«/.««.rf. 


HON.  JOHN  A.  FINCH,  the  well-known  insurance  lawyer  of  Indianapolis, 
in  a  recent  lecture  before  the  senior  class  of  the  Medical  College  of  Indiana  of  the 
University  of  Indianapolis,  commended  A  B  C  OF  LIFE  INSURANCE  as 
follows: 

If  your  interest  should  be  general  in  the  subject  (of  life  insurance),  so  that  you 
wish  to  know  something  of  the  principle  or  principles  which  underlie  the  business 
of  life  insurance,  I  know  of  no  better  work  to  recommend  you  to  than  a  little  book 
called  A  B  C  OF  LIFE  INSURANCE,  published  by  The  Spectator  Company, 
New  York.  There  is  also  a  book  by  M.  M.  Dawson,  entitled  ELEMENTS  OF 
LIFE  INSURANCE;  also  THREE  SYSTEMS  OF  LIFE  INSURANCE, 
both  by  the  same  publishers,  all  of  which  you  will  find  profitable. 

Mr.  Finch  has  also  given  the  following  endorsement  of  A  B  C  OF  LIFE 
INSURANCE : 

I  believe  I  have  in  my  office  as  nearly  a  complete  set  of  books  on  the  subject  of 
life  insurance  as  can  be  collected,  and  I  am  free  to  say  that  I  think  there  is  more 
meat  in  A  B  C  OF  LIFE  INSURANCE  than  in  any  single  book  for  the 
beginner  in  the  study  of  the  principles  of  life  insurance.  I  think  the  insurance 
companies  would  do  themselves  and  the  public  service  if  they  would  buy  this 
little  book  and  give  a  copy  to  each  student  in  the  law  schools  of  the  country.  I  am, 
perhaps,  a  little  over  hopeful,  but  I  believe  the  popular  impression  of  life  insurance 
as  reflected  in  the  decisions  of  the  courts  and  the  acts  of  our  legislatures  is  very 
largely  attributable  to  ignorance ;  and  I  believe  this  could  be  removed  by  proper 
missionary  work. 


I 


14  DAY  USE 

RETURN  TO  DESK  PROM  WHICH  BORROWED 

LOAN  DEPT. 

n:^^^tS^j^^:^'-Zdiate  recall 


(F7763sl0>476B 


.General  Library 

University  of  California 

Berkeley 


YClGbll^V 


